analysis.calculus.fderiv.add
β·
Mathlib.Analysis.Calculus.FDeriv.Add
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
@@ -3,8 +3,8 @@ 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.Linear
-import Analysis.Calculus.Fderiv.Comp
+import Analysis.Calculus.FDeriv.Linear
+import Analysis.Calculus.FDeriv.Comp
#align_import analysis.calculus.fderiv.add from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ 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.Linear
-import Mathbin.Analysis.Calculus.Fderiv.Comp
+import Analysis.Calculus.Fderiv.Linear
+import Analysis.Calculus.Fderiv.Comp
#align_import analysis.calculus.fderiv.add from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, SΓ©bastien GouΓ«zel, Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.calculus.fderiv.add
-! 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.Linear
import Mathbin.Analysis.Calculus.Fderiv.Comp
+#align_import analysis.calculus.fderiv.add from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
/-!
# Additive operations on derivatives
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -66,54 +66,74 @@ variable {R : Type _} [Semiring R] [Module R F] [SMulCommClass π R F] [Contin
/-! ### Derivative of a function multiplied by a constant -/
+#print HasStrictFDerivAt.const_smul /-
theorem HasStrictFDerivAt.const_smul (h : HasStrictFDerivAt f f' x) (c : R) :
HasStrictFDerivAt (fun x => c β’ f x) (c β’ f') x :=
(c β’ (1 : F βL[π] F)).HasStrictFDerivAt.comp x h
#align has_strict_fderiv_at.const_smul HasStrictFDerivAt.const_smul
+-/
+#print HasFDerivAtFilter.const_smul /-
theorem HasFDerivAtFilter.const_smul (h : HasFDerivAtFilter f f' x L) (c : R) :
HasFDerivAtFilter (fun x => c β’ f x) (c β’ f') x L :=
(c β’ (1 : F βL[π] F)).HasFDerivAtFilter.comp x h tendsto_map
#align has_fderiv_at_filter.const_smul HasFDerivAtFilter.const_smul
+-/
+#print HasFDerivWithinAt.const_smul /-
theorem HasFDerivWithinAt.const_smul (h : HasFDerivWithinAt f f' s x) (c : R) :
HasFDerivWithinAt (fun x => c β’ f x) (c β’ f') s x :=
h.const_smul c
#align has_fderiv_within_at.const_smul HasFDerivWithinAt.const_smul
+-/
+#print HasFDerivAt.const_smul /-
theorem HasFDerivAt.const_smul (h : HasFDerivAt f f' x) (c : R) :
HasFDerivAt (fun x => c β’ f x) (c β’ f') x :=
h.const_smul c
#align has_fderiv_at.const_smul HasFDerivAt.const_smul
+-/
+#print DifferentiableWithinAt.const_smul /-
theorem DifferentiableWithinAt.const_smul (h : DifferentiableWithinAt π f s x) (c : R) :
DifferentiableWithinAt π (fun y => c β’ f y) s x :=
(h.HasFDerivWithinAt.const_smul c).DifferentiableWithinAt
#align differentiable_within_at.const_smul DifferentiableWithinAt.const_smul
+-/
+#print DifferentiableAt.const_smul /-
theorem DifferentiableAt.const_smul (h : DifferentiableAt π f x) (c : R) :
DifferentiableAt π (fun y => c β’ f y) x :=
(h.HasFDerivAt.const_smul c).DifferentiableAt
#align differentiable_at.const_smul DifferentiableAt.const_smul
+-/
+#print DifferentiableOn.const_smul /-
theorem DifferentiableOn.const_smul (h : DifferentiableOn π f s) (c : R) :
DifferentiableOn π (fun y => c β’ f y) s := fun x hx => (h x hx).const_smul c
#align differentiable_on.const_smul DifferentiableOn.const_smul
+-/
+#print Differentiable.const_smul /-
theorem Differentiable.const_smul (h : Differentiable π f) (c : R) :
Differentiable π fun y => c β’ f y := fun x => (h x).const_smul c
#align differentiable.const_smul Differentiable.const_smul
+-/
+#print fderivWithin_const_smul /-
theorem fderivWithin_const_smul (hxs : UniqueDiffWithinAt π s x)
(h : DifferentiableWithinAt π f s x) (c : R) :
fderivWithin π (fun y => c β’ f y) s x = c β’ fderivWithin π f s x :=
(h.HasFDerivWithinAt.const_smul c).fderivWithin hxs
#align fderiv_within_const_smul fderivWithin_const_smul
+-/
+#print fderiv_const_smul /-
theorem fderiv_const_smul (h : DifferentiableAt π f x) (c : R) :
fderiv π (fun y => c β’ f y) x = c β’ fderiv π f x :=
(h.HasFDerivAt.const_smul c).fderiv
#align fderiv_const_smul fderiv_const_smul
+-/
end ConstSmul
@@ -122,121 +142,166 @@ section Add
/-! ### Derivative of the sum of two functions -/
+#print HasStrictFDerivAt.add /-
theorem HasStrictFDerivAt.add (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDerivAt g g' x) :
HasStrictFDerivAt (fun y => f y + g y) (f' + g') x :=
(hf.add hg).congr_left fun y => by
simp only [LinearMap.sub_apply, LinearMap.add_apply, map_sub, map_add, add_apply]; abel
#align has_strict_fderiv_at.add HasStrictFDerivAt.add
+-/
+#print HasFDerivAtFilter.add /-
theorem HasFDerivAtFilter.add (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivAtFilter g g' x L) :
HasFDerivAtFilter (fun y => f y + g y) (f' + g') x L :=
(hf.add hg).congr_left fun _ => by
simp only [LinearMap.sub_apply, LinearMap.add_apply, map_sub, map_add, add_apply]; abel
#align has_fderiv_at_filter.add HasFDerivAtFilter.add
+-/
+#print HasFDerivWithinAt.add /-
theorem HasFDerivWithinAt.add (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivWithinAt g g' s x) :
HasFDerivWithinAt (fun y => f y + g y) (f' + g') s x :=
hf.add hg
#align has_fderiv_within_at.add HasFDerivWithinAt.add
+-/
+#print HasFDerivAt.add /-
theorem HasFDerivAt.add (hf : HasFDerivAt f f' x) (hg : HasFDerivAt g g' x) :
HasFDerivAt (fun x => f x + g x) (f' + g') x :=
hf.add hg
#align has_fderiv_at.add HasFDerivAt.add
+-/
+#print DifferentiableWithinAt.add /-
theorem DifferentiableWithinAt.add (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) : DifferentiableWithinAt π (fun y => f y + g y) s x :=
(hf.HasFDerivWithinAt.add hg.HasFDerivWithinAt).DifferentiableWithinAt
#align differentiable_within_at.add DifferentiableWithinAt.add
+-/
+#print DifferentiableAt.add /-
@[simp]
theorem DifferentiableAt.add (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
DifferentiableAt π (fun y => f y + g y) x :=
(hf.HasFDerivAt.add hg.HasFDerivAt).DifferentiableAt
#align differentiable_at.add DifferentiableAt.add
+-/
+#print DifferentiableOn.add /-
theorem DifferentiableOn.add (hf : DifferentiableOn π f s) (hg : DifferentiableOn π g s) :
DifferentiableOn π (fun y => f y + g y) s := fun x hx => (hf x hx).add (hg x hx)
#align differentiable_on.add DifferentiableOn.add
+-/
+#print Differentiable.add /-
@[simp]
theorem Differentiable.add (hf : Differentiable π f) (hg : Differentiable π g) :
Differentiable π fun y => f y + g y := fun x => (hf x).add (hg x)
#align differentiable.add Differentiable.add
+-/
+#print fderivWithin_add /-
theorem fderivWithin_add (hxs : UniqueDiffWithinAt π s x) (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) :
fderivWithin π (fun y => f y + g y) s x = fderivWithin π f s x + fderivWithin π g s x :=
(hf.HasFDerivWithinAt.add hg.HasFDerivWithinAt).fderivWithin hxs
#align fderiv_within_add fderivWithin_add
+-/
+#print fderiv_add /-
theorem fderiv_add (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
fderiv π (fun y => f y + g y) x = fderiv π f x + fderiv π g x :=
(hf.HasFDerivAt.add hg.HasFDerivAt).fderiv
#align fderiv_add fderiv_add
+-/
+#print HasStrictFDerivAt.add_const /-
theorem HasStrictFDerivAt.add_const (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun y => f y + c) f' x :=
add_zero f' βΈ hf.add (hasStrictFDerivAt_const _ _)
#align has_strict_fderiv_at.add_const HasStrictFDerivAt.add_const
+-/
+#print HasFDerivAtFilter.add_const /-
theorem HasFDerivAtFilter.add_const (hf : HasFDerivAtFilter f f' x L) (c : F) :
HasFDerivAtFilter (fun y => f y + c) f' x L :=
add_zero f' βΈ hf.add (hasFDerivAtFilter_const _ _ _)
#align has_fderiv_at_filter.add_const HasFDerivAtFilter.add_const
+-/
+#print HasFDerivWithinAt.add_const /-
theorem HasFDerivWithinAt.add_const (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun y => f y + c) f' s x :=
hf.AddConst c
#align has_fderiv_within_at.add_const HasFDerivWithinAt.add_const
+-/
+#print HasFDerivAt.add_const /-
theorem HasFDerivAt.add_const (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => f x + c) f' x :=
hf.AddConst c
#align has_fderiv_at.add_const HasFDerivAt.add_const
+-/
+#print DifferentiableWithinAt.add_const /-
theorem DifferentiableWithinAt.add_const (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => f y + c) s x :=
(hf.HasFDerivWithinAt.AddConst c).DifferentiableWithinAt
#align differentiable_within_at.add_const DifferentiableWithinAt.add_const
+-/
+#print differentiableWithinAt_add_const_iff /-
@[simp]
theorem differentiableWithinAt_add_const_iff (c : F) :
DifferentiableWithinAt π (fun y => f y + c) s x β DifferentiableWithinAt π f s x :=
β¨fun h => by simpa using h.add_const (-c), fun h => h.AddConst cβ©
#align differentiable_within_at_add_const_iff differentiableWithinAt_add_const_iff
+-/
+#print DifferentiableAt.add_const /-
theorem DifferentiableAt.add_const (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => f y + c) x :=
(hf.HasFDerivAt.AddConst c).DifferentiableAt
#align differentiable_at.add_const DifferentiableAt.add_const
+-/
+#print differentiableAt_add_const_iff /-
@[simp]
theorem differentiableAt_add_const_iff (c : F) :
DifferentiableAt π (fun y => f y + c) x β DifferentiableAt π f x :=
β¨fun h => by simpa using h.add_const (-c), fun h => h.AddConst cβ©
#align differentiable_at_add_const_iff differentiableAt_add_const_iff
+-/
+#print DifferentiableOn.add_const /-
theorem DifferentiableOn.add_const (hf : DifferentiableOn π f s) (c : F) :
DifferentiableOn π (fun y => f y + c) s := fun x hx => (hf x hx).AddConst c
#align differentiable_on.add_const DifferentiableOn.add_const
+-/
+#print differentiableOn_add_const_iff /-
@[simp]
theorem differentiableOn_add_const_iff (c : F) :
DifferentiableOn π (fun y => f y + c) s β DifferentiableOn π f s :=
β¨fun h => by simpa using h.add_const (-c), fun h => h.AddConst cβ©
#align differentiable_on_add_const_iff differentiableOn_add_const_iff
+-/
+#print Differentiable.add_const /-
theorem Differentiable.add_const (hf : Differentiable π f) (c : F) :
Differentiable π fun y => f y + c := fun x => (hf x).AddConst c
#align differentiable.add_const Differentiable.add_const
+-/
+#print differentiable_add_const_iff /-
@[simp]
theorem differentiable_add_const_iff (c : F) :
(Differentiable π fun y => f y + c) β Differentiable π f :=
β¨fun h => by simpa using h.add_const (-c), fun h => h.AddConst cβ©
#align differentiable_add_const_iff differentiable_add_const_iff
+-/
+#print fderivWithin_add_const /-
theorem fderivWithin_add_const (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => f y + c) s x = fderivWithin π f s x :=
if hf : DifferentiableWithinAt π f s x then (hf.HasFDerivWithinAt.AddConst c).fderivWithin hxs
@@ -246,81 +311,112 @@ theorem fderivWithin_add_const (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin_zero_of_not_differentiableWithinAt]
simpa
#align fderiv_within_add_const fderivWithin_add_const
+-/
+#print fderiv_add_const /-
theorem fderiv_add_const (c : F) : fderiv π (fun y => f y + c) x = fderiv π f x := by
simp only [β fderivWithin_univ, fderivWithin_add_const uniqueDiffWithinAt_univ]
#align fderiv_add_const fderiv_add_const
+-/
+#print HasStrictFDerivAt.const_add /-
theorem HasStrictFDerivAt.const_add (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun y => c + f y) f' x :=
zero_add f' βΈ (hasStrictFDerivAt_const _ _).add hf
#align has_strict_fderiv_at.const_add HasStrictFDerivAt.const_add
+-/
+#print HasFDerivAtFilter.const_add /-
theorem HasFDerivAtFilter.const_add (hf : HasFDerivAtFilter f f' x L) (c : F) :
HasFDerivAtFilter (fun y => c + f y) f' x L :=
zero_add f' βΈ (hasFDerivAtFilter_const _ _ _).add hf
#align has_fderiv_at_filter.const_add HasFDerivAtFilter.const_add
+-/
+#print HasFDerivWithinAt.const_add /-
theorem HasFDerivWithinAt.const_add (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun y => c + f y) f' s x :=
hf.const_add c
#align has_fderiv_within_at.const_add HasFDerivWithinAt.const_add
+-/
+#print HasFDerivAt.const_add /-
theorem HasFDerivAt.const_add (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => c + f x) f' x :=
hf.const_add c
#align has_fderiv_at.const_add HasFDerivAt.const_add
+-/
+#print DifferentiableWithinAt.const_add /-
theorem DifferentiableWithinAt.const_add (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => c + f y) s x :=
(hf.HasFDerivWithinAt.const_add c).DifferentiableWithinAt
#align differentiable_within_at.const_add DifferentiableWithinAt.const_add
+-/
+#print differentiableWithinAt_const_add_iff /-
@[simp]
theorem differentiableWithinAt_const_add_iff (c : F) :
DifferentiableWithinAt π (fun y => c + f y) s x β DifferentiableWithinAt π f s x :=
β¨fun h => by simpa using h.const_add (-c), fun h => h.const_add cβ©
#align differentiable_within_at_const_add_iff differentiableWithinAt_const_add_iff
+-/
+#print DifferentiableAt.const_add /-
theorem DifferentiableAt.const_add (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => c + f y) x :=
(hf.HasFDerivAt.const_add c).DifferentiableAt
#align differentiable_at.const_add DifferentiableAt.const_add
+-/
+#print differentiableAt_const_add_iff /-
@[simp]
theorem differentiableAt_const_add_iff (c : F) :
DifferentiableAt π (fun y => c + f y) x β DifferentiableAt π f x :=
β¨fun h => by simpa using h.const_add (-c), fun h => h.const_add cβ©
#align differentiable_at_const_add_iff differentiableAt_const_add_iff
+-/
+#print DifferentiableOn.const_add /-
theorem DifferentiableOn.const_add (hf : DifferentiableOn π f s) (c : F) :
DifferentiableOn π (fun y => c + f y) s := fun x hx => (hf x hx).const_add c
#align differentiable_on.const_add DifferentiableOn.const_add
+-/
+#print differentiableOn_const_add_iff /-
@[simp]
theorem differentiableOn_const_add_iff (c : F) :
DifferentiableOn π (fun y => c + f y) s β DifferentiableOn π f s :=
β¨fun h => by simpa using h.const_add (-c), fun h => h.const_add cβ©
#align differentiable_on_const_add_iff differentiableOn_const_add_iff
+-/
+#print Differentiable.const_add /-
theorem Differentiable.const_add (hf : Differentiable π f) (c : F) :
Differentiable π fun y => c + f y := fun x => (hf x).const_add c
#align differentiable.const_add Differentiable.const_add
+-/
+#print differentiable_const_add_iff /-
@[simp]
theorem differentiable_const_add_iff (c : F) :
(Differentiable π fun y => c + f y) β Differentiable π f :=
β¨fun h => by simpa using h.const_add (-c), fun h => h.const_add cβ©
#align differentiable_const_add_iff differentiable_const_add_iff
+-/
+#print fderivWithin_const_add /-
theorem fderivWithin_const_add (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => c + f y) s x = fderivWithin π f s x := by
simpa only [add_comm] using fderivWithin_add_const hxs c
#align fderiv_within_const_add fderivWithin_const_add
+-/
+#print fderiv_const_add /-
theorem fderiv_const_add (c : F) : fderiv π (fun y => c + f y) x = fderiv π f x := by
simp only [add_comm c, fderiv_add_const]
#align fderiv_const_add fderiv_const_add
+-/
end Add
@@ -333,6 +429,7 @@ open scoped BigOperators
variable {ΞΉ : Type _} {u : Finset ΞΉ} {A : ΞΉ β E β F} {A' : ΞΉ β E βL[π] F}
+#print HasStrictFDerivAt.sum /-
theorem HasStrictFDerivAt.sum (h : β i β u, HasStrictFDerivAt (A i) (A' i) x) :
HasStrictFDerivAt (fun y => β i in u, A i y) (β i in u, A' i) x :=
by
@@ -340,7 +437,9 @@ theorem HasStrictFDerivAt.sum (h : β i β u, HasStrictFDerivAt (A i) (A' i) x
convert is_o.sum h
simp [Finset.sum_sub_distrib, ContinuousLinearMap.sum_apply]
#align has_strict_fderiv_at.sum HasStrictFDerivAt.sum
+-/
+#print HasFDerivAtFilter.sum /-
theorem HasFDerivAtFilter.sum (h : β i β u, HasFDerivAtFilter (A i) (A' i) x L) :
HasFDerivAtFilter (fun y => β i in u, A i y) (β i in u, A' i) x L :=
by
@@ -348,49 +447,66 @@ theorem HasFDerivAtFilter.sum (h : β i β u, HasFDerivAtFilter (A i) (A' i) x
convert is_o.sum h
simp [ContinuousLinearMap.sum_apply]
#align has_fderiv_at_filter.sum HasFDerivAtFilter.sum
+-/
+#print HasFDerivWithinAt.sum /-
theorem HasFDerivWithinAt.sum (h : β i β u, HasFDerivWithinAt (A i) (A' i) s x) :
HasFDerivWithinAt (fun y => β i in u, A i y) (β i in u, A' i) s x :=
HasFDerivAtFilter.sum h
#align has_fderiv_within_at.sum HasFDerivWithinAt.sum
+-/
+#print HasFDerivAt.sum /-
theorem HasFDerivAt.sum (h : β i β u, HasFDerivAt (A i) (A' i) x) :
HasFDerivAt (fun y => β i in u, A i y) (β i in u, A' i) x :=
HasFDerivAtFilter.sum h
#align has_fderiv_at.sum HasFDerivAt.sum
+-/
+#print DifferentiableWithinAt.sum /-
theorem DifferentiableWithinAt.sum (h : β i β u, DifferentiableWithinAt π (A i) s x) :
DifferentiableWithinAt π (fun y => β i in u, A i y) s x :=
HasFDerivWithinAt.differentiableWithinAt <|
HasFDerivWithinAt.sum fun i hi => (h i hi).HasFDerivWithinAt
#align differentiable_within_at.sum DifferentiableWithinAt.sum
+-/
+#print DifferentiableAt.sum /-
@[simp]
theorem DifferentiableAt.sum (h : β i β u, DifferentiableAt π (A i) x) :
DifferentiableAt π (fun y => β i in u, A i y) x :=
HasFDerivAt.differentiableAt <| HasFDerivAt.sum fun i hi => (h i hi).HasFDerivAt
#align differentiable_at.sum DifferentiableAt.sum
+-/
+#print DifferentiableOn.sum /-
theorem DifferentiableOn.sum (h : β i β u, DifferentiableOn π (A i) s) :
DifferentiableOn π (fun y => β i in u, A i y) s := fun x hx =>
DifferentiableWithinAt.sum fun i hi => h i hi x hx
#align differentiable_on.sum DifferentiableOn.sum
+-/
+#print Differentiable.sum /-
@[simp]
theorem Differentiable.sum (h : β i β u, Differentiable π (A i)) :
Differentiable π fun y => β i in u, A i y := fun x => DifferentiableAt.sum fun i hi => h i hi x
#align differentiable.sum Differentiable.sum
+-/
+#print fderivWithin_sum /-
theorem fderivWithin_sum (hxs : UniqueDiffWithinAt π s x)
(h : β i β u, DifferentiableWithinAt π (A i) s x) :
fderivWithin π (fun y => β i in u, A i y) s x = β i in u, fderivWithin π (A i) s x :=
(HasFDerivWithinAt.sum fun i hi => (h i hi).HasFDerivWithinAt).fderivWithin hxs
#align fderiv_within_sum fderivWithin_sum
+-/
+#print fderiv_sum /-
theorem fderiv_sum (h : β i β u, DifferentiableAt π (A i) x) :
fderiv π (fun y => β i in u, A i y) x = β i in u, fderiv π (A i) x :=
(HasFDerivAt.sum fun i hi => (h i hi).HasFDerivAt).fderiv
#align fderiv_sum fderiv_sum
+-/
end Sum
@@ -399,63 +515,88 @@ section Neg
/-! ### Derivative of the negative of a function -/
+#print HasStrictFDerivAt.neg /-
theorem HasStrictFDerivAt.neg (h : HasStrictFDerivAt f f' x) :
HasStrictFDerivAt (fun x => -f x) (-f') x :=
(-1 : F βL[π] F).HasStrictFDerivAt.comp x h
#align has_strict_fderiv_at.neg HasStrictFDerivAt.neg
+-/
+#print HasFDerivAtFilter.neg /-
theorem HasFDerivAtFilter.neg (h : HasFDerivAtFilter f f' x L) :
HasFDerivAtFilter (fun x => -f x) (-f') x L :=
(-1 : F βL[π] F).HasFDerivAtFilter.comp x h tendsto_map
#align has_fderiv_at_filter.neg HasFDerivAtFilter.neg
+-/
+#print HasFDerivWithinAt.neg /-
theorem HasFDerivWithinAt.neg (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt (fun x => -f x) (-f') s x :=
h.neg
#align has_fderiv_within_at.neg HasFDerivWithinAt.neg
+-/
+#print HasFDerivAt.neg /-
theorem HasFDerivAt.neg (h : HasFDerivAt f f' x) : HasFDerivAt (fun x => -f x) (-f') x :=
h.neg
#align has_fderiv_at.neg HasFDerivAt.neg
+-/
+#print DifferentiableWithinAt.neg /-
theorem DifferentiableWithinAt.neg (h : DifferentiableWithinAt π f s x) :
DifferentiableWithinAt π (fun y => -f y) s x :=
h.HasFDerivWithinAt.neg.DifferentiableWithinAt
#align differentiable_within_at.neg DifferentiableWithinAt.neg
+-/
+#print differentiableWithinAt_neg_iff /-
@[simp]
theorem differentiableWithinAt_neg_iff :
DifferentiableWithinAt π (fun y => -f y) s x β DifferentiableWithinAt π f s x :=
β¨fun h => by simpa only [neg_neg] using h.neg, fun h => h.negβ©
#align differentiable_within_at_neg_iff differentiableWithinAt_neg_iff
+-/
+#print DifferentiableAt.neg /-
theorem DifferentiableAt.neg (h : DifferentiableAt π f x) : DifferentiableAt π (fun y => -f y) x :=
h.HasFDerivAt.neg.DifferentiableAt
#align differentiable_at.neg DifferentiableAt.neg
+-/
+#print differentiableAt_neg_iff /-
@[simp]
theorem differentiableAt_neg_iff : DifferentiableAt π (fun y => -f y) x β DifferentiableAt π f x :=
β¨fun h => by simpa only [neg_neg] using h.neg, fun h => h.negβ©
#align differentiable_at_neg_iff differentiableAt_neg_iff
+-/
+#print DifferentiableOn.neg /-
theorem DifferentiableOn.neg (h : DifferentiableOn π f s) : DifferentiableOn π (fun y => -f y) s :=
fun x hx => (h x hx).neg
#align differentiable_on.neg DifferentiableOn.neg
+-/
+#print differentiableOn_neg_iff /-
@[simp]
theorem differentiableOn_neg_iff : DifferentiableOn π (fun y => -f y) s β DifferentiableOn π f s :=
β¨fun h => by simpa only [neg_neg] using h.neg, fun h => h.negβ©
#align differentiable_on_neg_iff differentiableOn_neg_iff
+-/
+#print Differentiable.neg /-
theorem Differentiable.neg (h : Differentiable π f) : Differentiable π fun y => -f y := fun x =>
(h x).neg
#align differentiable.neg Differentiable.neg
+-/
+#print differentiable_neg_iff /-
@[simp]
theorem differentiable_neg_iff : (Differentiable π fun y => -f y) β Differentiable π f :=
β¨fun h => by simpa only [neg_neg] using h.neg, fun h => h.negβ©
#align differentiable_neg_iff differentiable_neg_iff
+-/
+#print fderivWithin_neg /-
theorem fderivWithin_neg (hxs : UniqueDiffWithinAt π s x) :
fderivWithin π (fun y => -f y) s x = -fderivWithin π f s x :=
if h : DifferentiableWithinAt π f s x then h.HasFDerivWithinAt.neg.fderivWithin hxs
@@ -465,11 +606,14 @@ theorem fderivWithin_neg (hxs : UniqueDiffWithinAt π s x) :
fderivWithin_zero_of_not_differentiableWithinAt, neg_zero]
simpa
#align fderiv_within_neg fderivWithin_neg
+-/
+#print fderiv_neg /-
@[simp]
theorem fderiv_neg : fderiv π (fun y => -f y) x = -fderiv π f x := by
simp only [β fderivWithin_univ, fderivWithin_neg uniqueDiffWithinAt_univ]
#align fderiv_neg fderiv_neg
+-/
end Neg
@@ -478,195 +622,271 @@ section Sub
/-! ### Derivative of the difference of two functions -/
+#print HasStrictFDerivAt.sub /-
theorem HasStrictFDerivAt.sub (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDerivAt g g' x) :
HasStrictFDerivAt (fun x => f x - g x) (f' - g') x := by
simpa only [sub_eq_add_neg] using hf.add hg.neg
#align has_strict_fderiv_at.sub HasStrictFDerivAt.sub
+-/
+#print HasFDerivAtFilter.sub /-
theorem HasFDerivAtFilter.sub (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivAtFilter g g' x L) :
HasFDerivAtFilter (fun x => f x - g x) (f' - g') x L := by
simpa only [sub_eq_add_neg] using hf.add hg.neg
#align has_fderiv_at_filter.sub HasFDerivAtFilter.sub
+-/
+#print HasFDerivWithinAt.sub /-
theorem HasFDerivWithinAt.sub (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivWithinAt g g' s x) :
HasFDerivWithinAt (fun x => f x - g x) (f' - g') s x :=
hf.sub hg
#align has_fderiv_within_at.sub HasFDerivWithinAt.sub
+-/
+#print HasFDerivAt.sub /-
theorem HasFDerivAt.sub (hf : HasFDerivAt f f' x) (hg : HasFDerivAt g g' x) :
HasFDerivAt (fun x => f x - g x) (f' - g') x :=
hf.sub hg
#align has_fderiv_at.sub HasFDerivAt.sub
+-/
+#print DifferentiableWithinAt.sub /-
theorem DifferentiableWithinAt.sub (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) : DifferentiableWithinAt π (fun y => f y - g y) s x :=
(hf.HasFDerivWithinAt.sub hg.HasFDerivWithinAt).DifferentiableWithinAt
#align differentiable_within_at.sub DifferentiableWithinAt.sub
+-/
+#print DifferentiableAt.sub /-
@[simp]
theorem DifferentiableAt.sub (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
DifferentiableAt π (fun y => f y - g y) x :=
(hf.HasFDerivAt.sub hg.HasFDerivAt).DifferentiableAt
#align differentiable_at.sub DifferentiableAt.sub
+-/
+#print DifferentiableOn.sub /-
theorem DifferentiableOn.sub (hf : DifferentiableOn π f s) (hg : DifferentiableOn π g s) :
DifferentiableOn π (fun y => f y - g y) s := fun x hx => (hf x hx).sub (hg x hx)
#align differentiable_on.sub DifferentiableOn.sub
+-/
+#print Differentiable.sub /-
@[simp]
theorem Differentiable.sub (hf : Differentiable π f) (hg : Differentiable π g) :
Differentiable π fun y => f y - g y := fun x => (hf x).sub (hg x)
#align differentiable.sub Differentiable.sub
+-/
+#print fderivWithin_sub /-
theorem fderivWithin_sub (hxs : UniqueDiffWithinAt π s x) (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) :
fderivWithin π (fun y => f y - g y) s x = fderivWithin π f s x - fderivWithin π g s x :=
(hf.HasFDerivWithinAt.sub hg.HasFDerivWithinAt).fderivWithin hxs
#align fderiv_within_sub fderivWithin_sub
+-/
+#print fderiv_sub /-
theorem fderiv_sub (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
fderiv π (fun y => f y - g y) x = fderiv π f x - fderiv π g x :=
(hf.HasFDerivAt.sub hg.HasFDerivAt).fderiv
#align fderiv_sub fderiv_sub
+-/
+#print HasStrictFDerivAt.sub_const /-
theorem HasStrictFDerivAt.sub_const (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun x => f x - c) f' x := by
simpa only [sub_eq_add_neg] using hf.add_const (-c)
#align has_strict_fderiv_at.sub_const HasStrictFDerivAt.sub_const
+-/
+#print HasFDerivAtFilter.sub_const /-
theorem HasFDerivAtFilter.sub_const (hf : HasFDerivAtFilter f f' x L) (c : F) :
HasFDerivAtFilter (fun x => f x - c) f' x L := by
simpa only [sub_eq_add_neg] using hf.add_const (-c)
#align has_fderiv_at_filter.sub_const HasFDerivAtFilter.sub_const
+-/
+#print HasFDerivWithinAt.sub_const /-
theorem HasFDerivWithinAt.sub_const (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun x => f x - c) f' s x :=
hf.sub_const c
#align has_fderiv_within_at.sub_const HasFDerivWithinAt.sub_const
+-/
+#print HasFDerivAt.sub_const /-
theorem HasFDerivAt.sub_const (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => f x - c) f' x :=
hf.sub_const c
#align has_fderiv_at.sub_const HasFDerivAt.sub_const
+-/
+#print DifferentiableWithinAt.sub_const /-
theorem DifferentiableWithinAt.sub_const (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => f y - c) s x :=
(hf.HasFDerivWithinAt.sub_const c).DifferentiableWithinAt
#align differentiable_within_at.sub_const DifferentiableWithinAt.sub_const
+-/
+#print differentiableWithinAt_sub_const_iff /-
@[simp]
theorem differentiableWithinAt_sub_const_iff (c : F) :
DifferentiableWithinAt π (fun y => f y - c) s x β DifferentiableWithinAt π f s x := by
simp only [sub_eq_add_neg, differentiableWithinAt_add_const_iff]
#align differentiable_within_at_sub_const_iff differentiableWithinAt_sub_const_iff
+-/
+#print DifferentiableAt.sub_const /-
theorem DifferentiableAt.sub_const (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => f y - c) x :=
(hf.HasFDerivAt.sub_const c).DifferentiableAt
#align differentiable_at.sub_const DifferentiableAt.sub_const
+-/
+#print differentiableAt_sub_const_iff /-
@[simp]
theorem differentiableAt_sub_const_iff (c : F) :
DifferentiableAt π (fun y => f y - c) x β DifferentiableAt π f x := by
simp only [sub_eq_add_neg, differentiableAt_add_const_iff]
#align differentiable_at_sub_const_iff differentiableAt_sub_const_iff
+-/
+#print DifferentiableOn.sub_const /-
theorem DifferentiableOn.sub_const (hf : DifferentiableOn π f s) (c : F) :
DifferentiableOn π (fun y => f y - c) s := fun x hx => (hf x hx).sub_const c
#align differentiable_on.sub_const DifferentiableOn.sub_const
+-/
+#print differentiableOn_sub_const_iff /-
@[simp]
theorem differentiableOn_sub_const_iff (c : F) :
DifferentiableOn π (fun y => f y - c) s β DifferentiableOn π f s := by
simp only [sub_eq_add_neg, differentiableOn_add_const_iff]
#align differentiable_on_sub_const_iff differentiableOn_sub_const_iff
+-/
+#print Differentiable.sub_const /-
theorem Differentiable.sub_const (hf : Differentiable π f) (c : F) :
Differentiable π fun y => f y - c := fun x => (hf x).sub_const c
#align differentiable.sub_const Differentiable.sub_const
+-/
+#print differentiable_sub_const_iff /-
@[simp]
theorem differentiable_sub_const_iff (c : F) :
(Differentiable π fun y => f y - c) β Differentiable π f := by
simp only [sub_eq_add_neg, differentiable_add_const_iff]
#align differentiable_sub_const_iff differentiable_sub_const_iff
+-/
+#print fderivWithin_sub_const /-
theorem fderivWithin_sub_const (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => f y - c) s x = fderivWithin π f s x := by
simp only [sub_eq_add_neg, fderivWithin_add_const hxs]
#align fderiv_within_sub_const fderivWithin_sub_const
+-/
+#print fderiv_sub_const /-
theorem fderiv_sub_const (c : F) : fderiv π (fun y => f y - c) x = fderiv π f x := by
simp only [sub_eq_add_neg, fderiv_add_const]
#align fderiv_sub_const fderiv_sub_const
+-/
+#print HasStrictFDerivAt.const_sub /-
theorem HasStrictFDerivAt.const_sub (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun x => c - f x) (-f') x := by
simpa only [sub_eq_add_neg] using hf.neg.const_add c
#align has_strict_fderiv_at.const_sub HasStrictFDerivAt.const_sub
+-/
+#print HasFDerivAtFilter.const_sub /-
theorem HasFDerivAtFilter.const_sub (hf : HasFDerivAtFilter f f' x L) (c : F) :
HasFDerivAtFilter (fun x => c - f x) (-f') x L := by
simpa only [sub_eq_add_neg] using hf.neg.const_add c
#align has_fderiv_at_filter.const_sub HasFDerivAtFilter.const_sub
+-/
+#print HasFDerivWithinAt.const_sub /-
theorem HasFDerivWithinAt.const_sub (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun x => c - f x) (-f') s x :=
hf.const_sub c
#align has_fderiv_within_at.const_sub HasFDerivWithinAt.const_sub
+-/
+#print HasFDerivAt.const_sub /-
theorem HasFDerivAt.const_sub (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => c - f x) (-f') x :=
hf.const_sub c
#align has_fderiv_at.const_sub HasFDerivAt.const_sub
+-/
+#print DifferentiableWithinAt.const_sub /-
theorem DifferentiableWithinAt.const_sub (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => c - f y) s x :=
(hf.HasFDerivWithinAt.const_sub c).DifferentiableWithinAt
#align differentiable_within_at.const_sub DifferentiableWithinAt.const_sub
+-/
+#print differentiableWithinAt_const_sub_iff /-
@[simp]
theorem differentiableWithinAt_const_sub_iff (c : F) :
DifferentiableWithinAt π (fun y => c - f y) s x β DifferentiableWithinAt π f s x := by
simp [sub_eq_add_neg]
#align differentiable_within_at_const_sub_iff differentiableWithinAt_const_sub_iff
+-/
+#print DifferentiableAt.const_sub /-
theorem DifferentiableAt.const_sub (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => c - f y) x :=
(hf.HasFDerivAt.const_sub c).DifferentiableAt
#align differentiable_at.const_sub DifferentiableAt.const_sub
+-/
+#print differentiableAt_const_sub_iff /-
@[simp]
theorem differentiableAt_const_sub_iff (c : F) :
DifferentiableAt π (fun y => c - f y) x β DifferentiableAt π f x := by simp [sub_eq_add_neg]
#align differentiable_at_const_sub_iff differentiableAt_const_sub_iff
+-/
+#print DifferentiableOn.const_sub /-
theorem DifferentiableOn.const_sub (hf : DifferentiableOn π f s) (c : F) :
DifferentiableOn π (fun y => c - f y) s := fun x hx => (hf x hx).const_sub c
#align differentiable_on.const_sub DifferentiableOn.const_sub
+-/
+#print differentiableOn_const_sub_iff /-
@[simp]
theorem differentiableOn_const_sub_iff (c : F) :
DifferentiableOn π (fun y => c - f y) s β DifferentiableOn π f s := by simp [sub_eq_add_neg]
#align differentiable_on_const_sub_iff differentiableOn_const_sub_iff
+-/
+#print Differentiable.const_sub /-
theorem Differentiable.const_sub (hf : Differentiable π f) (c : F) :
Differentiable π fun y => c - f y := fun x => (hf x).const_sub c
#align differentiable.const_sub Differentiable.const_sub
+-/
+#print differentiable_const_sub_iff /-
@[simp]
theorem differentiable_const_sub_iff (c : F) :
(Differentiable π fun y => c - f y) β Differentiable π f := by simp [sub_eq_add_neg]
#align differentiable_const_sub_iff differentiable_const_sub_iff
+-/
+#print fderivWithin_const_sub /-
theorem fderivWithin_const_sub (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => c - f y) s x = -fderivWithin π f s x := by
simp only [sub_eq_add_neg, fderivWithin_const_add, fderivWithin_neg, hxs]
#align fderiv_within_const_sub fderivWithin_const_sub
+-/
+#print fderiv_const_sub /-
theorem fderiv_const_sub (c : F) : fderiv π (fun y => c - f y) x = -fderiv π f x := by
simp only [β fderivWithin_univ, fderivWithin_const_sub uniqueDiffWithinAt_univ]
#align fderiv_const_sub fderiv_const_sub
+-/
end Sub
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -31,7 +31,7 @@ This file contains the usual formulas (and existence assertions) for the derivat
open Filter Asymptotics ContinuousLinearMap Set Metric
-open Topology Classical NNReal Filter Asymptotics ENNReal
+open scoped Topology Classical NNReal Filter Asymptotics ENNReal
noncomputable section
@@ -329,7 +329,7 @@ section Sum
/-! ### Derivative of a finite sum of functions -/
-open BigOperators
+open scoped BigOperators
variable {ΞΉ : Type _} {u : Finset ΞΉ} {A : ΞΉ β E β F} {A' : ΞΉ β E βL[π] F}
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -66,80 +66,50 @@ variable {R : Type _} [Semiring R] [Module R F] [SMulCommClass π R F] [Contin
/-! ### Derivative of a function multiplied by a constant -/
-/- warning: has_strict_fderiv_at.const_smul -> HasStrictFDerivAt.const_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.const_smul HasStrictFDerivAt.const_smulβ'. -/
theorem HasStrictFDerivAt.const_smul (h : HasStrictFDerivAt f f' x) (c : R) :
HasStrictFDerivAt (fun x => c β’ f x) (c β’ f') x :=
(c β’ (1 : F βL[π] F)).HasStrictFDerivAt.comp x h
#align has_strict_fderiv_at.const_smul HasStrictFDerivAt.const_smul
-/- warning: has_fderiv_at_filter.const_smul -> HasFDerivAtFilter.const_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.const_smul HasFDerivAtFilter.const_smulβ'. -/
theorem HasFDerivAtFilter.const_smul (h : HasFDerivAtFilter f f' x L) (c : R) :
HasFDerivAtFilter (fun x => c β’ f x) (c β’ f') x L :=
(c β’ (1 : F βL[π] F)).HasFDerivAtFilter.comp x h tendsto_map
#align has_fderiv_at_filter.const_smul HasFDerivAtFilter.const_smul
-/- warning: has_fderiv_within_at.const_smul -> HasFDerivWithinAt.const_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.const_smul HasFDerivWithinAt.const_smulβ'. -/
theorem HasFDerivWithinAt.const_smul (h : HasFDerivWithinAt f f' s x) (c : R) :
HasFDerivWithinAt (fun x => c β’ f x) (c β’ f') s x :=
h.const_smul c
#align has_fderiv_within_at.const_smul HasFDerivWithinAt.const_smul
-/- warning: has_fderiv_at.const_smul -> HasFDerivAt.const_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at.const_smul HasFDerivAt.const_smulβ'. -/
theorem HasFDerivAt.const_smul (h : HasFDerivAt f f' x) (c : R) :
HasFDerivAt (fun x => c β’ f x) (c β’ f') x :=
h.const_smul c
#align has_fderiv_at.const_smul HasFDerivAt.const_smul
-/- warning: differentiable_within_at.const_smul -> DifferentiableWithinAt.const_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable_within_at.const_smul DifferentiableWithinAt.const_smulβ'. -/
theorem DifferentiableWithinAt.const_smul (h : DifferentiableWithinAt π f s x) (c : R) :
DifferentiableWithinAt π (fun y => c β’ f y) s x :=
(h.HasFDerivWithinAt.const_smul c).DifferentiableWithinAt
#align differentiable_within_at.const_smul DifferentiableWithinAt.const_smul
-/- warning: differentiable_at.const_smul -> DifferentiableAt.const_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable_at.const_smul DifferentiableAt.const_smulβ'. -/
theorem DifferentiableAt.const_smul (h : DifferentiableAt π f x) (c : R) :
DifferentiableAt π (fun y => c β’ f y) x :=
(h.HasFDerivAt.const_smul c).DifferentiableAt
#align differentiable_at.const_smul DifferentiableAt.const_smul
-/- warning: differentiable_on.const_smul -> DifferentiableOn.const_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable_on.const_smul DifferentiableOn.const_smulβ'. -/
theorem DifferentiableOn.const_smul (h : DifferentiableOn π f s) (c : R) :
DifferentiableOn π (fun y => c β’ f y) s := fun x hx => (h x hx).const_smul c
#align differentiable_on.const_smul DifferentiableOn.const_smul
-/- warning: differentiable.const_smul -> Differentiable.const_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable.const_smul Differentiable.const_smulβ'. -/
theorem Differentiable.const_smul (h : Differentiable π f) (c : R) :
Differentiable π fun y => c β’ f y := fun x => (h x).const_smul c
#align differentiable.const_smul Differentiable.const_smul
-/- warning: fderiv_within_const_smul -> fderivWithin_const_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_within_const_smul fderivWithin_const_smulβ'. -/
theorem fderivWithin_const_smul (hxs : UniqueDiffWithinAt π s x)
(h : DifferentiableWithinAt π f s x) (c : R) :
fderivWithin π (fun y => c β’ f y) s x = c β’ fderivWithin π f s x :=
(h.HasFDerivWithinAt.const_smul c).fderivWithin hxs
#align fderiv_within_const_smul fderivWithin_const_smul
-/- warning: fderiv_const_smul -> fderiv_const_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_const_smul fderiv_const_smulβ'. -/
theorem fderiv_const_smul (h : DifferentiableAt π f x) (c : R) :
fderiv π (fun y => c β’ f y) x = c β’ fderiv π f x :=
(h.HasFDerivAt.const_smul c).fderiv
@@ -152,238 +122,121 @@ section Add
/-! ### Derivative of the sum of two functions -/
-/- warning: has_strict_fderiv_at.add -> HasStrictFDerivAt.add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.add HasStrictFDerivAt.addβ'. -/
theorem HasStrictFDerivAt.add (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDerivAt g g' x) :
HasStrictFDerivAt (fun y => f y + g y) (f' + g') x :=
(hf.add hg).congr_left fun y => by
simp only [LinearMap.sub_apply, LinearMap.add_apply, map_sub, map_add, add_apply]; abel
#align has_strict_fderiv_at.add HasStrictFDerivAt.add
-/- warning: has_fderiv_at_filter.add -> HasFDerivAtFilter.add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.add HasFDerivAtFilter.addβ'. -/
theorem HasFDerivAtFilter.add (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivAtFilter g g' x L) :
HasFDerivAtFilter (fun y => f y + g y) (f' + g') x L :=
(hf.add hg).congr_left fun _ => by
simp only [LinearMap.sub_apply, LinearMap.add_apply, map_sub, map_add, add_apply]; abel
#align has_fderiv_at_filter.add HasFDerivAtFilter.add
-/- warning: has_fderiv_within_at.add -> HasFDerivWithinAt.add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.add HasFDerivWithinAt.addβ'. -/
theorem HasFDerivWithinAt.add (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivWithinAt g g' s x) :
HasFDerivWithinAt (fun y => f y + g y) (f' + g') s x :=
hf.add hg
#align has_fderiv_within_at.add HasFDerivWithinAt.add
-/- warning: has_fderiv_at.add -> HasFDerivAt.add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at.add HasFDerivAt.addβ'. -/
theorem HasFDerivAt.add (hf : HasFDerivAt f f' x) (hg : HasFDerivAt g g' x) :
HasFDerivAt (fun x => f x + g x) (f' + g') x :=
hf.add hg
#align has_fderiv_at.add HasFDerivAt.add
-/- warning: differentiable_within_at.add -> DifferentiableWithinAt.add is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) s x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) s x)
-Case conversion may be inaccurate. Consider using '#align differentiable_within_at.add DifferentiableWithinAt.addβ'. -/
theorem DifferentiableWithinAt.add (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) : DifferentiableWithinAt π (fun y => f y + g y) s x :=
(hf.HasFDerivWithinAt.add hg.HasFDerivWithinAt).DifferentiableWithinAt
#align differentiable_within_at.add DifferentiableWithinAt.add
-/- warning: differentiable_at.add -> DifferentiableAt.add is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) x)
-Case conversion may be inaccurate. Consider using '#align differentiable_at.add DifferentiableAt.addβ'. -/
@[simp]
theorem DifferentiableAt.add (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
DifferentiableAt π (fun y => f y + g y) x :=
(hf.HasFDerivAt.add hg.HasFDerivAt).DifferentiableAt
#align differentiable_at.add DifferentiableAt.add
-/- warning: differentiable_on.add -> DifferentiableOn.add is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) s)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) s)
-Case conversion may be inaccurate. Consider using '#align differentiable_on.add DifferentiableOn.addβ'. -/
theorem DifferentiableOn.add (hf : DifferentiableOn π f s) (hg : DifferentiableOn π g s) :
DifferentiableOn π (fun y => f y + g y) s := fun x hx => (hf x hx).add (hg x hx)
#align differentiable_on.add DifferentiableOn.add
-/- warning: differentiable.add -> Differentiable.add is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F}, (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)))
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F}, (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)))
-Case conversion may be inaccurate. Consider using '#align differentiable.add Differentiable.addβ'. -/
@[simp]
theorem Differentiable.add (hf : Differentiable π f) (hg : Differentiable π g) :
Differentiable π fun y => f y + g y := fun x => (hf x).add (hg x)
#align differentiable.add Differentiable.add
-/- warning: fderiv_within_add -> fderivWithin_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_within_add fderivWithin_addβ'. -/
theorem fderivWithin_add (hxs : UniqueDiffWithinAt π s x) (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) :
fderivWithin π (fun y => f y + g y) s x = fderivWithin π f s x + fderivWithin π g s x :=
(hf.HasFDerivWithinAt.add hg.HasFDerivWithinAt).fderivWithin hxs
#align fderiv_within_add fderivWithin_add
-/- warning: fderiv_add -> fderiv_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_add fderiv_addβ'. -/
theorem fderiv_add (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
fderiv π (fun y => f y + g y) x = fderiv π f x + fderiv π g x :=
(hf.HasFDerivAt.add hg.HasFDerivAt).fderiv
#align fderiv_add fderiv_add
-/- warning: has_strict_fderiv_at.add_const -> HasStrictFDerivAt.add_const is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) f' x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) f' x)
-Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.add_const HasStrictFDerivAt.add_constβ'. -/
theorem HasStrictFDerivAt.add_const (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun y => f y + c) f' x :=
add_zero f' βΈ hf.add (hasStrictFDerivAt_const _ _)
#align has_strict_fderiv_at.add_const HasStrictFDerivAt.add_const
-/- warning: has_fderiv_at_filter.add_const -> HasFDerivAtFilter.add_const is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) f' x L)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) f' x L)
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.add_const HasFDerivAtFilter.add_constβ'. -/
theorem HasFDerivAtFilter.add_const (hf : HasFDerivAtFilter f f' x L) (c : F) :
HasFDerivAtFilter (fun y => f y + c) f' x L :=
add_zero f' βΈ hf.add (hasFDerivAtFilter_const _ _ _)
#align has_fderiv_at_filter.add_const HasFDerivAtFilter.add_const
-/- warning: has_fderiv_within_at.add_const -> HasFDerivWithinAt.add_const is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) f' s x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) f' s x)
-Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.add_const HasFDerivWithinAt.add_constβ'. -/
theorem HasFDerivWithinAt.add_const (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun y => f y + c) f' s x :=
hf.AddConst c
#align has_fderiv_within_at.add_const HasFDerivWithinAt.add_const
-/- warning: has_fderiv_at.add_const -> HasFDerivAt.add_const is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f x) c) f' x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f x) c) f' x)
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at.add_const HasFDerivAt.add_constβ'. -/
theorem HasFDerivAt.add_const (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => f x + c) f' x :=
hf.AddConst c
#align has_fderiv_at.add_const HasFDerivAt.add_const
-/- warning: differentiable_within_at.add_const -> DifferentiableWithinAt.add_const is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : F), DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) s x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : F), DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) s x)
-Case conversion may be inaccurate. Consider using '#align differentiable_within_at.add_const DifferentiableWithinAt.add_constβ'. -/
theorem DifferentiableWithinAt.add_const (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => f y + c) s x :=
(hf.HasFDerivWithinAt.AddConst c).DifferentiableWithinAt
#align differentiable_within_at.add_const DifferentiableWithinAt.add_const
-/- warning: differentiable_within_at_add_const_iff -> differentiableWithinAt_add_const_iff is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (c : F), Iff (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) s x) (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)
-Case conversion may be inaccurate. Consider using '#align differentiable_within_at_add_const_iff differentiableWithinAt_add_const_iffβ'. -/
@[simp]
theorem differentiableWithinAt_add_const_iff (c : F) :
DifferentiableWithinAt π (fun y => f y + c) s x β DifferentiableWithinAt π f s x :=
β¨fun h => by simpa using h.add_const (-c), fun h => h.AddConst cβ©
#align differentiable_within_at_add_const_iff differentiableWithinAt_add_const_iff
-/- warning: differentiable_at.add_const -> DifferentiableAt.add_const is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : F), DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : F), DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) x)
-Case conversion may be inaccurate. Consider using '#align differentiable_at.add_const DifferentiableAt.add_constβ'. -/
theorem DifferentiableAt.add_const (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => f y + c) x :=
(hf.HasFDerivAt.AddConst c).DifferentiableAt
#align differentiable_at.add_const DifferentiableAt.add_const
-/- warning: differentiable_at_add_const_iff -> differentiableAt_add_const_iff is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} (c : F), Iff (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) x) (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} (c : F), Iff (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) x) (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
-Case conversion may be inaccurate. Consider using '#align differentiable_at_add_const_iff differentiableAt_add_const_iffβ'. -/
@[simp]
theorem differentiableAt_add_const_iff (c : F) :
DifferentiableAt π (fun y => f y + c) x β DifferentiableAt π f x :=
β¨fun h => by simpa using h.add_const (-c), fun h => h.AddConst cβ©
#align differentiable_at_add_const_iff differentiableAt_add_const_iff
-/- warning: differentiable_on.add_const -> DifferentiableOn.add_const is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (forall (c : F), DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) s)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (forall (c : F), DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) s)
-Case conversion may be inaccurate. Consider using '#align differentiable_on.add_const DifferentiableOn.add_constβ'. -/
theorem DifferentiableOn.add_const (hf : DifferentiableOn π f s) (c : F) :
DifferentiableOn π (fun y => f y + c) s := fun x hx => (hf x hx).AddConst c
#align differentiable_on.add_const DifferentiableOn.add_const
-/- warning: differentiable_on_add_const_iff -> differentiableOn_add_const_iff is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {s : Set.{u2} E} (c : F), Iff (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) s) (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {s : Set.{u2} E} (c : F), Iff (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) s) (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s)
-Case conversion may be inaccurate. Consider using '#align differentiable_on_add_const_iff differentiableOn_add_const_iffβ'. -/
@[simp]
theorem differentiableOn_add_const_iff (c : F) :
DifferentiableOn π (fun y => f y + c) s β DifferentiableOn π f s :=
β¨fun h => by simpa using h.add_const (-c), fun h => h.AddConst cβ©
#align differentiable_on_add_const_iff differentiableOn_add_const_iff
-/- warning: differentiable.add_const -> Differentiable.add_const is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F}, (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (forall (c : F), Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c))
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- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F}, (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (forall (c : F), Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c))
-Case conversion may be inaccurate. Consider using '#align differentiable.add_const Differentiable.add_constβ'. -/
theorem Differentiable.add_const (hf : Differentiable π f) (c : F) :
Differentiable π fun y => f y + c := fun x => (hf x).AddConst c
#align differentiable.add_const Differentiable.add_const
-/- warning: differentiable_add_const_iff -> differentiable_add_const_iff is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} (c : F), Iff (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c)) (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} (c : F), Iff (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c)) (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
-Case conversion may be inaccurate. Consider using '#align differentiable_add_const_iff differentiable_add_const_iffβ'. -/
@[simp]
theorem differentiable_add_const_iff (c : F) :
(Differentiable π fun y => f y + c) β Differentiable π f :=
β¨fun h => by simpa using h.add_const (-c), fun h => h.AddConst cβ©
#align differentiable_add_const_iff differentiable_add_const_iff
-/- warning: fderiv_within_add_const -> fderivWithin_add_const is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_within_add_const fderivWithin_add_constβ'. -/
theorem fderivWithin_add_const (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => f y + c) s x = fderivWithin π f s x :=
if hf : DifferentiableWithinAt π f s x then (hf.HasFDerivWithinAt.AddConst c).fderivWithin hxs
@@ -394,158 +247,77 @@ theorem fderivWithin_add_const (hxs : UniqueDiffWithinAt π s x) (c : F) :
simpa
#align fderiv_within_add_const fderivWithin_add_const
-/- warning: fderiv_add_const -> fderiv_add_const is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_add_const fderiv_add_constβ'. -/
theorem fderiv_add_const (c : F) : fderiv π (fun y => f y + c) x = fderiv π f x := by
simp only [β fderivWithin_univ, fderivWithin_add_const uniqueDiffWithinAt_univ]
#align fderiv_add_const fderiv_add_const
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- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y)) f' x)
-Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.const_add HasStrictFDerivAt.const_addβ'. -/
theorem HasStrictFDerivAt.const_add (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun y => c + f y) f' x :=
zero_add f' βΈ (hasStrictFDerivAt_const _ _).add hf
#align has_strict_fderiv_at.const_add HasStrictFDerivAt.const_add
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- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y)) f' x L)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y)) f' x L)
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.const_add HasFDerivAtFilter.const_addβ'. -/
theorem HasFDerivAtFilter.const_add (hf : HasFDerivAtFilter f f' x L) (c : F) :
HasFDerivAtFilter (fun y => c + f y) f' x L :=
zero_add f' βΈ (hasFDerivAtFilter_const _ _ _).add hf
#align has_fderiv_at_filter.const_add HasFDerivAtFilter.const_add
-/- warning: has_fderiv_within_at.const_add -> HasFDerivWithinAt.const_add is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y)) f' s x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y)) f' s x)
-Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.const_add HasFDerivWithinAt.const_addβ'. -/
theorem HasFDerivWithinAt.const_add (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun y => c + f y) f' s x :=
hf.const_add c
#align has_fderiv_within_at.const_add HasFDerivWithinAt.const_add
-/- warning: has_fderiv_at.const_add -> HasFDerivAt.const_add is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f x)) f' x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f x)) f' x)
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at.const_add HasFDerivAt.const_addβ'. -/
theorem HasFDerivAt.const_add (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => c + f x) f' x :=
hf.const_add c
#align has_fderiv_at.const_add HasFDerivAt.const_add
-/- warning: differentiable_within_at.const_add -> DifferentiableWithinAt.const_add is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align differentiable_within_at.const_add DifferentiableWithinAt.const_addβ'. -/
theorem DifferentiableWithinAt.const_add (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => c + f y) s x :=
(hf.HasFDerivWithinAt.const_add c).DifferentiableWithinAt
#align differentiable_within_at.const_add DifferentiableWithinAt.const_add
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@[simp]
theorem differentiableWithinAt_const_add_iff (c : F) :
DifferentiableWithinAt π (fun y => c + f y) s x β DifferentiableWithinAt π f s x :=
β¨fun h => by simpa using h.const_add (-c), fun h => h.const_add cβ©
#align differentiable_within_at_const_add_iff differentiableWithinAt_const_add_iff
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-Case conversion may be inaccurate. Consider using '#align differentiable_at.const_add DifferentiableAt.const_addβ'. -/
theorem DifferentiableAt.const_add (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => c + f y) x :=
(hf.HasFDerivAt.const_add c).DifferentiableAt
#align differentiable_at.const_add DifferentiableAt.const_add
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@[simp]
theorem differentiableAt_const_add_iff (c : F) :
DifferentiableAt π (fun y => c + f y) x β DifferentiableAt π f x :=
β¨fun h => by simpa using h.const_add (-c), fun h => h.const_add cβ©
#align differentiable_at_const_add_iff differentiableAt_const_add_iff
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-Case conversion may be inaccurate. Consider using '#align differentiable_on.const_add DifferentiableOn.const_addβ'. -/
theorem DifferentiableOn.const_add (hf : DifferentiableOn π f s) (c : F) :
DifferentiableOn π (fun y => c + f y) s := fun x hx => (hf x hx).const_add c
#align differentiable_on.const_add DifferentiableOn.const_add
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@[simp]
theorem differentiableOn_const_add_iff (c : F) :
DifferentiableOn π (fun y => c + f y) s β DifferentiableOn π f s :=
β¨fun h => by simpa using h.const_add (-c), fun h => h.const_add cβ©
#align differentiable_on_const_add_iff differentiableOn_const_add_iff
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theorem Differentiable.const_add (hf : Differentiable π f) (c : F) :
Differentiable π fun y => c + f y := fun x => (hf x).const_add c
#align differentiable.const_add Differentiable.const_add
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- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} (c : F), Iff (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y))) (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} (c : F), Iff (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y))) (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
-Case conversion may be inaccurate. Consider using '#align differentiable_const_add_iff differentiable_const_add_iffβ'. -/
@[simp]
theorem differentiable_const_add_iff (c : F) :
(Differentiable π fun y => c + f y) β Differentiable π f :=
β¨fun h => by simpa using h.const_add (-c), fun h => h.const_add cβ©
#align differentiable_const_add_iff differentiable_const_add_iff
-/- warning: fderiv_within_const_add -> fderivWithin_const_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_within_const_add fderivWithin_const_addβ'. -/
theorem fderivWithin_const_add (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => c + f y) s x = fderivWithin π f s x := by
simpa only [add_comm] using fderivWithin_add_const hxs c
#align fderiv_within_const_add fderivWithin_const_add
-/- warning: fderiv_const_add -> fderiv_const_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_const_add fderiv_const_addβ'. -/
theorem fderiv_const_add (c : F) : fderiv π (fun y => c + f y) x = fderiv π f x := by
simp only [add_comm c, fderiv_add_const]
#align fderiv_const_add fderiv_const_add
@@ -561,9 +333,6 @@ open BigOperators
variable {ΞΉ : Type _} {u : Finset ΞΉ} {A : ΞΉ β E β F} {A' : ΞΉ β E βL[π] F}
-/- warning: has_strict_fderiv_at.sum -> HasStrictFDerivAt.sum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.sum HasStrictFDerivAt.sumβ'. -/
theorem HasStrictFDerivAt.sum (h : β i β u, HasStrictFDerivAt (A i) (A' i) x) :
HasStrictFDerivAt (fun y => β i in u, A i y) (β i in u, A' i) x :=
by
@@ -572,9 +341,6 @@ theorem HasStrictFDerivAt.sum (h : β i β u, HasStrictFDerivAt (A i) (A' i) x
simp [Finset.sum_sub_distrib, ContinuousLinearMap.sum_apply]
#align has_strict_fderiv_at.sum HasStrictFDerivAt.sum
-/- warning: has_fderiv_at_filter.sum -> HasFDerivAtFilter.sum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.sum HasFDerivAtFilter.sumβ'. -/
theorem HasFDerivAtFilter.sum (h : β i β u, HasFDerivAtFilter (A i) (A' i) x L) :
HasFDerivAtFilter (fun y => β i in u, A i y) (β i in u, A' i) x L :=
by
@@ -583,80 +349,44 @@ theorem HasFDerivAtFilter.sum (h : β i β u, HasFDerivAtFilter (A i) (A' i) x
simp [ContinuousLinearMap.sum_apply]
#align has_fderiv_at_filter.sum HasFDerivAtFilter.sum
-/- warning: has_fderiv_within_at.sum -> HasFDerivWithinAt.sum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.sum HasFDerivWithinAt.sumβ'. -/
theorem HasFDerivWithinAt.sum (h : β i β u, HasFDerivWithinAt (A i) (A' i) s x) :
HasFDerivWithinAt (fun y => β i in u, A i y) (β i in u, A' i) s x :=
HasFDerivAtFilter.sum h
#align has_fderiv_within_at.sum HasFDerivWithinAt.sum
-/- warning: has_fderiv_at.sum -> HasFDerivAt.sum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at.sum HasFDerivAt.sumβ'. -/
theorem HasFDerivAt.sum (h : β i β u, HasFDerivAt (A i) (A' i) x) :
HasFDerivAt (fun y => β i in u, A i y) (β i in u, A' i) x :=
HasFDerivAtFilter.sum h
#align has_fderiv_at.sum HasFDerivAt.sum
-/- warning: differentiable_within_at.sum -> DifferentiableWithinAt.sum is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) s x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) s x)
-Case conversion may be inaccurate. Consider using '#align differentiable_within_at.sum DifferentiableWithinAt.sumβ'. -/
theorem DifferentiableWithinAt.sum (h : β i β u, DifferentiableWithinAt π (A i) s x) :
DifferentiableWithinAt π (fun y => β i in u, A i y) s x :=
HasFDerivWithinAt.differentiableWithinAt <|
HasFDerivWithinAt.sum fun i hi => (h i hi).HasFDerivWithinAt
#align differentiable_within_at.sum DifferentiableWithinAt.sum
-/- warning: differentiable_at.sum -> DifferentiableAt.sum is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) x)
-Case conversion may be inaccurate. Consider using '#align differentiable_at.sum DifferentiableAt.sumβ'. -/
@[simp]
theorem DifferentiableAt.sum (h : β i β u, DifferentiableAt π (A i) x) :
DifferentiableAt π (fun y => β i in u, A i y) x :=
HasFDerivAt.differentiableAt <| HasFDerivAt.sum fun i hi => (h i hi).HasFDerivAt
#align differentiable_at.sum DifferentiableAt.sum
-/- warning: differentiable_on.sum -> DifferentiableOn.sum is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s)) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) s)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s)) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) s)
-Case conversion may be inaccurate. Consider using '#align differentiable_on.sum DifferentiableOn.sumβ'. -/
theorem DifferentiableOn.sum (h : β i β u, DifferentiableOn π (A i) s) :
DifferentiableOn π (fun y => β i in u, A i y) s := fun x hx =>
DifferentiableWithinAt.sum fun i hi => h i hi x hx
#align differentiable_on.sum DifferentiableOn.sum
-/- warning: differentiable.sum -> Differentiable.sum is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i))) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)))
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i))) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)))
-Case conversion may be inaccurate. Consider using '#align differentiable.sum Differentiable.sumβ'. -/
@[simp]
theorem Differentiable.sum (h : β i β u, Differentiable π (A i)) :
Differentiable π fun y => β i in u, A i y := fun x => DifferentiableAt.sum fun i hi => h i hi x
#align differentiable.sum Differentiable.sum
-/- warning: fderiv_within_sum -> fderivWithin_sum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_within_sum fderivWithin_sumβ'. -/
theorem fderivWithin_sum (hxs : UniqueDiffWithinAt π s x)
(h : β i β u, DifferentiableWithinAt π (A i) s x) :
fderivWithin π (fun y => β i in u, A i y) s x = β i in u, fderivWithin π (A i) s x :=
(HasFDerivWithinAt.sum fun i hi => (h i hi).HasFDerivWithinAt).fderivWithin hxs
#align fderiv_within_sum fderivWithin_sum
-/- warning: fderiv_sum -> fderiv_sum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_sum fderiv_sumβ'. -/
theorem fderiv_sum (h : β i β u, DifferentiableAt π (A i) x) :
fderiv π (fun y => β i in u, A i y) x = β i in u, fderiv π (A i) x :=
(HasFDerivAt.sum fun i hi => (h i hi).HasFDerivAt).fderiv
@@ -669,126 +399,63 @@ section Neg
/-! ### Derivative of the negative of a function -/
-/- warning: has_strict_fderiv_at.neg -> HasStrictFDerivAt.neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.neg HasStrictFDerivAt.negβ'. -/
theorem HasStrictFDerivAt.neg (h : HasStrictFDerivAt f f' x) :
HasStrictFDerivAt (fun x => -f x) (-f') x :=
(-1 : F βL[π] F).HasStrictFDerivAt.comp x h
#align has_strict_fderiv_at.neg HasStrictFDerivAt.neg
-/- warning: has_fderiv_at_filter.neg -> HasFDerivAtFilter.neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.neg HasFDerivAtFilter.negβ'. -/
theorem HasFDerivAtFilter.neg (h : HasFDerivAtFilter f f' x L) :
HasFDerivAtFilter (fun x => -f x) (-f') x L :=
(-1 : F βL[π] F).HasFDerivAtFilter.comp x h tendsto_map
#align has_fderiv_at_filter.neg HasFDerivAtFilter.neg
-/- warning: has_fderiv_within_at.neg -> HasFDerivWithinAt.neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.neg HasFDerivWithinAt.negβ'. -/
theorem HasFDerivWithinAt.neg (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt (fun x => -f x) (-f') s x :=
h.neg
#align has_fderiv_within_at.neg HasFDerivWithinAt.neg
-/- warning: has_fderiv_at.neg -> HasFDerivAt.neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at.neg HasFDerivAt.negβ'. -/
theorem HasFDerivAt.neg (h : HasFDerivAt f f' x) : HasFDerivAt (fun x => -f x) (-f') x :=
h.neg
#align has_fderiv_at.neg HasFDerivAt.neg
-/- warning: differentiable_within_at.neg -> DifferentiableWithinAt.neg is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align differentiable_within_at.neg DifferentiableWithinAt.negβ'. -/
theorem DifferentiableWithinAt.neg (h : DifferentiableWithinAt π f s x) :
DifferentiableWithinAt π (fun y => -f y) s x :=
h.HasFDerivWithinAt.neg.DifferentiableWithinAt
#align differentiable_within_at.neg DifferentiableWithinAt.neg
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-Case conversion may be inaccurate. Consider using '#align differentiable_within_at_neg_iff differentiableWithinAt_neg_iffβ'. -/
@[simp]
theorem differentiableWithinAt_neg_iff :
DifferentiableWithinAt π (fun y => -f y) s x β DifferentiableWithinAt π f s x :=
β¨fun h => by simpa only [neg_neg] using h.neg, fun h => h.negβ©
#align differentiable_within_at_neg_iff differentiableWithinAt_neg_iff
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-Case conversion may be inaccurate. Consider using '#align differentiable_at.neg DifferentiableAt.negβ'. -/
theorem DifferentiableAt.neg (h : DifferentiableAt π f x) : DifferentiableAt π (fun y => -f y) x :=
h.HasFDerivAt.neg.DifferentiableAt
#align differentiable_at.neg DifferentiableAt.neg
-/- warning: differentiable_at_neg_iff -> differentiableAt_neg_iff is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align differentiable_at_neg_iff differentiableAt_neg_iffβ'. -/
@[simp]
theorem differentiableAt_neg_iff : DifferentiableAt π (fun y => -f y) x β DifferentiableAt π f x :=
β¨fun h => by simpa only [neg_neg] using h.neg, fun h => h.negβ©
#align differentiable_at_neg_iff differentiableAt_neg_iff
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-Case conversion may be inaccurate. Consider using '#align differentiable_on.neg DifferentiableOn.negβ'. -/
theorem DifferentiableOn.neg (h : DifferentiableOn π f s) : DifferentiableOn π (fun y => -f y) s :=
fun x hx => (h x hx).neg
#align differentiable_on.neg DifferentiableOn.neg
-/- warning: differentiable_on_neg_iff -> differentiableOn_neg_iff is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align differentiable_on_neg_iff differentiableOn_neg_iffβ'. -/
@[simp]
theorem differentiableOn_neg_iff : DifferentiableOn π (fun y => -f y) s β DifferentiableOn π f s :=
β¨fun h => by simpa only [neg_neg] using h.neg, fun h => h.negβ©
#align differentiable_on_neg_iff differentiableOn_neg_iff
-/- warning: differentiable.neg -> Differentiable.neg is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align differentiable.neg Differentiable.negβ'. -/
theorem Differentiable.neg (h : Differentiable π f) : Differentiable π fun y => -f y := fun x =>
(h x).neg
#align differentiable.neg Differentiable.neg
-/- warning: differentiable_neg_iff -> differentiable_neg_iff is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align differentiable_neg_iff differentiable_neg_iffβ'. -/
@[simp]
theorem differentiable_neg_iff : (Differentiable π fun y => -f y) β Differentiable π f :=
β¨fun h => by simpa only [neg_neg] using h.neg, fun h => h.negβ©
#align differentiable_neg_iff differentiable_neg_iff
-/- warning: fderiv_within_neg -> fderivWithin_neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_within_neg fderivWithin_negβ'. -/
theorem fderivWithin_neg (hxs : UniqueDiffWithinAt π s x) :
fderivWithin π (fun y => -f y) s x = -fderivWithin π f s x :=
if h : DifferentiableWithinAt π f s x then h.HasFDerivWithinAt.neg.fderivWithin hxs
@@ -799,9 +466,6 @@ theorem fderivWithin_neg (hxs : UniqueDiffWithinAt π s x) :
simpa
#align fderiv_within_neg fderivWithin_neg
-/- warning: fderiv_neg -> fderiv_neg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_neg fderiv_negβ'. -/
@[simp]
theorem fderiv_neg : fderiv π (fun y => -f y) x = -fderiv π f x := by
simp only [β fderivWithin_univ, fderivWithin_neg uniqueDiffWithinAt_univ]
@@ -814,378 +478,192 @@ section Sub
/-! ### Derivative of the difference of two functions -/
-/- warning: has_strict_fderiv_at.sub -> HasStrictFDerivAt.sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.sub HasStrictFDerivAt.subβ'. -/
theorem HasStrictFDerivAt.sub (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDerivAt g g' x) :
HasStrictFDerivAt (fun x => f x - g x) (f' - g') x := by
simpa only [sub_eq_add_neg] using hf.add hg.neg
#align has_strict_fderiv_at.sub HasStrictFDerivAt.sub
-/- warning: has_fderiv_at_filter.sub -> HasFDerivAtFilter.sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.sub HasFDerivAtFilter.subβ'. -/
theorem HasFDerivAtFilter.sub (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivAtFilter g g' x L) :
HasFDerivAtFilter (fun x => f x - g x) (f' - g') x L := by
simpa only [sub_eq_add_neg] using hf.add hg.neg
#align has_fderiv_at_filter.sub HasFDerivAtFilter.sub
-/- warning: has_fderiv_within_at.sub -> HasFDerivWithinAt.sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.sub HasFDerivWithinAt.subβ'. -/
theorem HasFDerivWithinAt.sub (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivWithinAt g g' s x) :
HasFDerivWithinAt (fun x => f x - g x) (f' - g') s x :=
hf.sub hg
#align has_fderiv_within_at.sub HasFDerivWithinAt.sub
-/- warning: has_fderiv_at.sub -> HasFDerivAt.sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at.sub HasFDerivAt.subβ'. -/
theorem HasFDerivAt.sub (hf : HasFDerivAt f f' x) (hg : HasFDerivAt g g' x) :
HasFDerivAt (fun x => f x - g x) (f' - g') x :=
hf.sub hg
#align has_fderiv_at.sub HasFDerivAt.sub
-/- warning: differentiable_within_at.sub -> DifferentiableWithinAt.sub is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) (g y)) s x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) (g y)) s x)
-Case conversion may be inaccurate. Consider using '#align differentiable_within_at.sub DifferentiableWithinAt.subβ'. -/
theorem DifferentiableWithinAt.sub (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) : DifferentiableWithinAt π (fun y => f y - g y) s x :=
(hf.HasFDerivWithinAt.sub hg.HasFDerivWithinAt).DifferentiableWithinAt
#align differentiable_within_at.sub DifferentiableWithinAt.sub
-/- warning: differentiable_at.sub -> DifferentiableAt.sub is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) (g y)) x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) (g y)) x)
-Case conversion may be inaccurate. Consider using '#align differentiable_at.sub DifferentiableAt.subβ'. -/
@[simp]
theorem DifferentiableAt.sub (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
DifferentiableAt π (fun y => f y - g y) x :=
(hf.HasFDerivAt.sub hg.HasFDerivAt).DifferentiableAt
#align differentiable_at.sub DifferentiableAt.sub
-/- warning: differentiable_on.sub -> DifferentiableOn.sub is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) (g y)) s)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) (g y)) s)
-Case conversion may be inaccurate. Consider using '#align differentiable_on.sub DifferentiableOn.subβ'. -/
theorem DifferentiableOn.sub (hf : DifferentiableOn π f s) (hg : DifferentiableOn π g s) :
DifferentiableOn π (fun y => f y - g y) s := fun x hx => (hf x hx).sub (hg x hx)
#align differentiable_on.sub DifferentiableOn.sub
-/- warning: differentiable.sub -> Differentiable.sub is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F}, (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) (g y)))
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F}, (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) (g y)))
-Case conversion may be inaccurate. Consider using '#align differentiable.sub Differentiable.subβ'. -/
@[simp]
theorem Differentiable.sub (hf : Differentiable π f) (hg : Differentiable π g) :
Differentiable π fun y => f y - g y := fun x => (hf x).sub (hg x)
#align differentiable.sub Differentiable.sub
-/- warning: fderiv_within_sub -> fderivWithin_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_within_sub fderivWithin_subβ'. -/
theorem fderivWithin_sub (hxs : UniqueDiffWithinAt π s x) (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) :
fderivWithin π (fun y => f y - g y) s x = fderivWithin π f s x - fderivWithin π g s x :=
(hf.HasFDerivWithinAt.sub hg.HasFDerivWithinAt).fderivWithin hxs
#align fderiv_within_sub fderivWithin_sub
-/- warning: fderiv_sub -> fderiv_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_sub fderiv_subβ'. -/
theorem fderiv_sub (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
fderiv π (fun y => f y - g y) x = fderiv π f x - fderiv π g x :=
(hf.HasFDerivAt.sub hg.HasFDerivAt).fderiv
#align fderiv_sub fderiv_sub
-/- warning: has_strict_fderiv_at.sub_const -> HasStrictFDerivAt.sub_const is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) c) f' x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) c) f' x)
-Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.sub_const HasStrictFDerivAt.sub_constβ'. -/
theorem HasStrictFDerivAt.sub_const (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun x => f x - c) f' x := by
simpa only [sub_eq_add_neg] using hf.add_const (-c)
#align has_strict_fderiv_at.sub_const HasStrictFDerivAt.sub_const
-/- warning: has_fderiv_at_filter.sub_const -> HasFDerivAtFilter.sub_const is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) c) f' x L)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) c) f' x L)
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.sub_const HasFDerivAtFilter.sub_constβ'. -/
theorem HasFDerivAtFilter.sub_const (hf : HasFDerivAtFilter f f' x L) (c : F) :
HasFDerivAtFilter (fun x => f x - c) f' x L := by
simpa only [sub_eq_add_neg] using hf.add_const (-c)
#align has_fderiv_at_filter.sub_const HasFDerivAtFilter.sub_const
-/- warning: has_fderiv_within_at.sub_const -> HasFDerivWithinAt.sub_const is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) c) f' s x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) c) f' s x)
-Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.sub_const HasFDerivWithinAt.sub_constβ'. -/
theorem HasFDerivWithinAt.sub_const (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun x => f x - c) f' s x :=
hf.sub_const c
#align has_fderiv_within_at.sub_const HasFDerivWithinAt.sub_const
-/- warning: has_fderiv_at.sub_const -> HasFDerivAt.sub_const is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) c) f' x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) c) f' x)
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at.sub_const HasFDerivAt.sub_constβ'. -/
theorem HasFDerivAt.sub_const (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => f x - c) f' x :=
hf.sub_const c
#align has_fderiv_at.sub_const HasFDerivAt.sub_const
-/- warning: differentiable_within_at.sub_const -> DifferentiableWithinAt.sub_const is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : F), DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) c) s x)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align differentiable_within_at.sub_const DifferentiableWithinAt.sub_constβ'. -/
theorem DifferentiableWithinAt.sub_const (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => f y - c) s x :=
(hf.HasFDerivWithinAt.sub_const c).DifferentiableWithinAt
#align differentiable_within_at.sub_const DifferentiableWithinAt.sub_const
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-Case conversion may be inaccurate. Consider using '#align differentiable_within_at_sub_const_iff differentiableWithinAt_sub_const_iffβ'. -/
@[simp]
theorem differentiableWithinAt_sub_const_iff (c : F) :
DifferentiableWithinAt π (fun y => f y - c) s x β DifferentiableWithinAt π f s x := by
simp only [sub_eq_add_neg, differentiableWithinAt_add_const_iff]
#align differentiable_within_at_sub_const_iff differentiableWithinAt_sub_const_iff
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-Case conversion may be inaccurate. Consider using '#align differentiable_at.sub_const DifferentiableAt.sub_constβ'. -/
theorem DifferentiableAt.sub_const (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => f y - c) x :=
(hf.HasFDerivAt.sub_const c).DifferentiableAt
#align differentiable_at.sub_const DifferentiableAt.sub_const
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-Case conversion may be inaccurate. Consider using '#align differentiable_at_sub_const_iff differentiableAt_sub_const_iffβ'. -/
@[simp]
theorem differentiableAt_sub_const_iff (c : F) :
DifferentiableAt π (fun y => f y - c) x β DifferentiableAt π f x := by
simp only [sub_eq_add_neg, differentiableAt_add_const_iff]
#align differentiable_at_sub_const_iff differentiableAt_sub_const_iff
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align differentiable_on.sub_const DifferentiableOn.sub_constβ'. -/
theorem DifferentiableOn.sub_const (hf : DifferentiableOn π f s) (c : F) :
DifferentiableOn π (fun y => f y - c) s := fun x hx => (hf x hx).sub_const c
#align differentiable_on.sub_const DifferentiableOn.sub_const
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align differentiable_on_sub_const_iff differentiableOn_sub_const_iffβ'. -/
@[simp]
theorem differentiableOn_sub_const_iff (c : F) :
DifferentiableOn π (fun y => f y - c) s β DifferentiableOn π f s := by
simp only [sub_eq_add_neg, differentiableOn_add_const_iff]
#align differentiable_on_sub_const_iff differentiableOn_sub_const_iff
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align differentiable.sub_const Differentiable.sub_constβ'. -/
theorem Differentiable.sub_const (hf : Differentiable π f) (c : F) :
Differentiable π fun y => f y - c := fun x => (hf x).sub_const c
#align differentiable.sub_const Differentiable.sub_const
-/- warning: differentiable_sub_const_iff -> differentiable_sub_const_iff is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align differentiable_sub_const_iff differentiable_sub_const_iffβ'. -/
@[simp]
theorem differentiable_sub_const_iff (c : F) :
(Differentiable π fun y => f y - c) β Differentiable π f := by
simp only [sub_eq_add_neg, differentiable_add_const_iff]
#align differentiable_sub_const_iff differentiable_sub_const_iff
-/- warning: fderiv_within_sub_const -> fderivWithin_sub_const is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_within_sub_const fderivWithin_sub_constβ'. -/
theorem fderivWithin_sub_const (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => f y - c) s x = fderivWithin π f s x := by
simp only [sub_eq_add_neg, fderivWithin_add_const hxs]
#align fderiv_within_sub_const fderivWithin_sub_const
-/- warning: fderiv_sub_const -> fderiv_sub_const is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_sub_const fderiv_sub_constβ'. -/
theorem fderiv_sub_const (c : F) : fderiv π (fun y => f y - c) x = fderiv π f x := by
simp only [sub_eq_add_neg, fderiv_add_const]
#align fderiv_sub_const fderiv_sub_const
-/- warning: has_strict_fderiv_at.const_sub -> HasStrictFDerivAt.const_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.const_sub HasStrictFDerivAt.const_subβ'. -/
theorem HasStrictFDerivAt.const_sub (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun x => c - f x) (-f') x := by
simpa only [sub_eq_add_neg] using hf.neg.const_add c
#align has_strict_fderiv_at.const_sub HasStrictFDerivAt.const_sub
-/- warning: has_fderiv_at_filter.const_sub -> HasFDerivAtFilter.const_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.const_sub HasFDerivAtFilter.const_subβ'. -/
theorem HasFDerivAtFilter.const_sub (hf : HasFDerivAtFilter f f' x L) (c : F) :
HasFDerivAtFilter (fun x => c - f x) (-f') x L := by
simpa only [sub_eq_add_neg] using hf.neg.const_add c
#align has_fderiv_at_filter.const_sub HasFDerivAtFilter.const_sub
-/- warning: has_fderiv_within_at.const_sub -> HasFDerivWithinAt.const_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.const_sub HasFDerivWithinAt.const_subβ'. -/
theorem HasFDerivWithinAt.const_sub (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun x => c - f x) (-f') s x :=
hf.const_sub c
#align has_fderiv_within_at.const_sub HasFDerivWithinAt.const_sub
-/- warning: has_fderiv_at.const_sub -> HasFDerivAt.const_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at.const_sub HasFDerivAt.const_subβ'. -/
theorem HasFDerivAt.const_sub (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => c - f x) (-f') x :=
hf.const_sub c
#align has_fderiv_at.const_sub HasFDerivAt.const_sub
-/- warning: differentiable_within_at.const_sub -> DifferentiableWithinAt.const_sub is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align differentiable_within_at.const_sub DifferentiableWithinAt.const_subβ'. -/
theorem DifferentiableWithinAt.const_sub (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => c - f y) s x :=
(hf.HasFDerivWithinAt.const_sub c).DifferentiableWithinAt
#align differentiable_within_at.const_sub DifferentiableWithinAt.const_sub
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-Case conversion may be inaccurate. Consider using '#align differentiable_within_at_const_sub_iff differentiableWithinAt_const_sub_iffβ'. -/
@[simp]
theorem differentiableWithinAt_const_sub_iff (c : F) :
DifferentiableWithinAt π (fun y => c - f y) s x β DifferentiableWithinAt π f s x := by
simp [sub_eq_add_neg]
#align differentiable_within_at_const_sub_iff differentiableWithinAt_const_sub_iff
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-Case conversion may be inaccurate. Consider using '#align differentiable_at.const_sub DifferentiableAt.const_subβ'. -/
theorem DifferentiableAt.const_sub (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => c - f y) x :=
(hf.HasFDerivAt.const_sub c).DifferentiableAt
#align differentiable_at.const_sub DifferentiableAt.const_sub
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-Case conversion may be inaccurate. Consider using '#align differentiable_at_const_sub_iff differentiableAt_const_sub_iffβ'. -/
@[simp]
theorem differentiableAt_const_sub_iff (c : F) :
DifferentiableAt π (fun y => c - f y) x β DifferentiableAt π f x := by simp [sub_eq_add_neg]
#align differentiable_at_const_sub_iff differentiableAt_const_sub_iff
-/- warning: differentiable_on.const_sub -> DifferentiableOn.const_sub is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align differentiable_on.const_sub DifferentiableOn.const_subβ'. -/
theorem DifferentiableOn.const_sub (hf : DifferentiableOn π f s) (c : F) :
DifferentiableOn π (fun y => c - f y) s := fun x hx => (hf x hx).const_sub c
#align differentiable_on.const_sub DifferentiableOn.const_sub
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align differentiable_on_const_sub_iff differentiableOn_const_sub_iffβ'. -/
@[simp]
theorem differentiableOn_const_sub_iff (c : F) :
DifferentiableOn π (fun y => c - f y) s β DifferentiableOn π f s := by simp [sub_eq_add_neg]
#align differentiable_on_const_sub_iff differentiableOn_const_sub_iff
-/- warning: differentiable.const_sub -> Differentiable.const_sub is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F}, (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (forall (c : F), Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y)))
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F}, (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (forall (c : F), Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f y)))
-Case conversion may be inaccurate. Consider using '#align differentiable.const_sub Differentiable.const_subβ'. -/
theorem Differentiable.const_sub (hf : Differentiable π f) (c : F) :
Differentiable π fun y => c - f y := fun x => (hf x).const_sub c
#align differentiable.const_sub Differentiable.const_sub
-/- warning: differentiable_const_sub_iff -> differentiable_const_sub_iff is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} (c : F), Iff (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y))) (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} (c : F), Iff (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f y))) (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
-Case conversion may be inaccurate. Consider using '#align differentiable_const_sub_iff differentiable_const_sub_iffβ'. -/
@[simp]
theorem differentiable_const_sub_iff (c : F) :
(Differentiable π fun y => c - f y) β Differentiable π f := by simp [sub_eq_add_neg]
#align differentiable_const_sub_iff differentiable_const_sub_iff
-/- warning: fderiv_within_const_sub -> fderivWithin_const_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_within_const_sub fderivWithin_const_subβ'. -/
theorem fderivWithin_const_sub (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => c - f y) s x = -fderivWithin π f s x := by
simp only [sub_eq_add_neg, fderivWithin_const_add, fderivWithin_neg, hxs]
#align fderiv_within_const_sub fderivWithin_const_sub
-/- warning: fderiv_const_sub -> fderiv_const_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_const_sub fderiv_const_subβ'. -/
theorem fderiv_const_sub (c : F) : fderiv π (fun y => c - f y) x = -fderiv π f x := by
simp only [β fderivWithin_univ, fderivWithin_const_sub uniqueDiffWithinAt_univ]
#align fderiv_const_sub fderiv_const_sub
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -157,10 +157,8 @@ section Add
Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.add HasStrictFDerivAt.addβ'. -/
theorem HasStrictFDerivAt.add (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDerivAt g g' x) :
HasStrictFDerivAt (fun y => f y + g y) (f' + g') x :=
- (hf.add hg).congr_left fun y =>
- by
- simp only [LinearMap.sub_apply, LinearMap.add_apply, map_sub, map_add, add_apply]
- abel
+ (hf.add hg).congr_left fun y => by
+ simp only [LinearMap.sub_apply, LinearMap.add_apply, map_sub, map_add, add_apply]; abel
#align has_strict_fderiv_at.add HasStrictFDerivAt.add
/- warning: has_fderiv_at_filter.add -> HasFDerivAtFilter.add is a dubious translation:
@@ -168,10 +166,8 @@ theorem HasStrictFDerivAt.add (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDe
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.add HasFDerivAtFilter.addβ'. -/
theorem HasFDerivAtFilter.add (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivAtFilter g g' x L) :
HasFDerivAtFilter (fun y => f y + g y) (f' + g') x L :=
- (hf.add hg).congr_left fun _ =>
- by
- simp only [LinearMap.sub_apply, LinearMap.add_apply, map_sub, map_add, add_apply]
- abel
+ (hf.add hg).congr_left fun _ => by
+ simp only [LinearMap.sub_apply, LinearMap.add_apply, map_sub, map_add, add_apply]; abel
#align has_fderiv_at_filter.add HasFDerivAtFilter.add
/- warning: has_fderiv_within_at.add -> HasFDerivWithinAt.add is a dubious translation:
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -67,10 +67,7 @@ variable {R : Type _} [Semiring R] [Module R F] [SMulCommClass π R F] [Contin
/- warning: has_strict_fderiv_at.const_smul -> HasStrictFDerivAt.const_smul is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : R), HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f x)) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c f') x)
-but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {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_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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)} {x : E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (HasStrictFDerivAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : R), HasStrictFDerivAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f x)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c f') x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.const_smul HasStrictFDerivAt.const_smulβ'. -/
theorem HasStrictFDerivAt.const_smul (h : HasStrictFDerivAt f f' x) (c : R) :
HasStrictFDerivAt (fun x => c β’ f x) (c β’ f') x :=
@@ -78,10 +75,7 @@ theorem HasStrictFDerivAt.const_smul (h : HasStrictFDerivAt f f' x) (c : R) :
#align has_strict_fderiv_at.const_smul HasStrictFDerivAt.const_smul
/- warning: has_fderiv_at_filter.const_smul -> HasFDerivAtFilter.const_smul is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : R), HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f x)) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c f') x L)
-but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {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_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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)} {x : E} {L : Filter.{u3} E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (HasFDerivAtFilter.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : R), HasFDerivAtFilter.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f x)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c f') x L)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.const_smul HasFDerivAtFilter.const_smulβ'. -/
theorem HasFDerivAtFilter.const_smul (h : HasFDerivAtFilter f f' x L) (c : R) :
HasFDerivAtFilter (fun x => c β’ f x) (c β’ f') x L :=
@@ -89,10 +83,7 @@ theorem HasFDerivAtFilter.const_smul (h : HasFDerivAtFilter f f' x L) (c : R) :
#align has_fderiv_at_filter.const_smul HasFDerivAtFilter.const_smul
/- warning: has_fderiv_within_at.const_smul -> HasFDerivWithinAt.const_smul is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : R), HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f x)) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c f') s x)
-but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {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_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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)} {x : E} {s : Set.{u3} E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (HasFDerivWithinAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : R), HasFDerivWithinAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f x)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c f') s x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.const_smul HasFDerivWithinAt.const_smulβ'. -/
theorem HasFDerivWithinAt.const_smul (h : HasFDerivWithinAt f f' s x) (c : R) :
HasFDerivWithinAt (fun x => c β’ f x) (c β’ f') s x :=
@@ -100,10 +91,7 @@ theorem HasFDerivWithinAt.const_smul (h : HasFDerivWithinAt f f' s x) (c : R) :
#align has_fderiv_within_at.const_smul HasFDerivWithinAt.const_smul
/- warning: has_fderiv_at.const_smul -> HasFDerivAt.const_smul is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : R), HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f x)) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c f') x)
-but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {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_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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)} {x : E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (HasFDerivAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : R), HasFDerivAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f x)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c f') x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at.const_smul HasFDerivAt.const_smulβ'. -/
theorem HasFDerivAt.const_smul (h : HasFDerivAt f f' x) (c : R) :
HasFDerivAt (fun x => c β’ f x) (c β’ f') x :=
@@ -111,10 +99,7 @@ theorem HasFDerivAt.const_smul (h : HasFDerivAt f f' x) (c : R) :
#align has_fderiv_at.const_smul HasFDerivAt.const_smul
/- warning: differentiable_within_at.const_smul -> DifferentiableWithinAt.const_smul is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : R), DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f y)) s x)
-but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u3} E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (DifferentiableWithinAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : R), DifferentiableWithinAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f y)) s x)
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable_within_at.const_smul DifferentiableWithinAt.const_smulβ'. -/
theorem DifferentiableWithinAt.const_smul (h : DifferentiableWithinAt π f s x) (c : R) :
DifferentiableWithinAt π (fun y => c β’ f y) s x :=
@@ -122,10 +107,7 @@ theorem DifferentiableWithinAt.const_smul (h : DifferentiableWithinAt π f s x
#align differentiable_within_at.const_smul DifferentiableWithinAt.const_smul
/- warning: differentiable_at.const_smul -> DifferentiableAt.const_smul is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : R), DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f y)) x)
-but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (DifferentiableAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : R), DifferentiableAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f y)) x)
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable_at.const_smul DifferentiableAt.const_smulβ'. -/
theorem DifferentiableAt.const_smul (h : DifferentiableAt π f x) (c : R) :
DifferentiableAt π (fun y => c β’ f y) x :=
@@ -133,30 +115,21 @@ theorem DifferentiableAt.const_smul (h : DifferentiableAt π f x) (c : R) :
#align differentiable_at.const_smul DifferentiableAt.const_smul
/- warning: differentiable_on.const_smul -> DifferentiableOn.const_smul is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {s : Set.{u2} E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (forall (c : R), DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f y)) s)
-but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {s : Set.{u3} E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (DifferentiableOn.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (forall (c : R), DifferentiableOn.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f y)) s)
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable_on.const_smul DifferentiableOn.const_smulβ'. -/
theorem DifferentiableOn.const_smul (h : DifferentiableOn π f s) (c : R) :
DifferentiableOn π (fun y => c β’ f y) s := fun x hx => (h x hx).const_smul c
#align differentiable_on.const_smul DifferentiableOn.const_smul
/- warning: differentiable.const_smul -> Differentiable.const_smul is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (forall (c : R), Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f y)))
-but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (Differentiable.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (forall (c : R), Differentiable.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f y)))
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable.const_smul Differentiable.const_smulβ'. -/
theorem Differentiable.const_smul (h : Differentiable π f) (c : R) :
Differentiable π fun y => c β’ f y := fun x => (h x).const_smul c
#align differentiable.const_smul Differentiable.const_smul
/- warning: fderiv_within_const_smul -> fderivWithin_const_smul is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : R), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f y)) s x) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
-but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u3} E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (UniqueDiffWithinAt.{u4, u3} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : R), Eq.{max (succ u3) (succ u2)} (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderivWithin.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f y)) s x) (HSMul.hSMul.{u1, max u2 u3, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c (fderivWithin.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_within_const_smul fderivWithin_const_smulβ'. -/
theorem fderivWithin_const_smul (hxs : UniqueDiffWithinAt π s x)
(h : DifferentiableWithinAt π f s x) (c : R) :
@@ -165,10 +138,7 @@ theorem fderivWithin_const_smul (hxs : UniqueDiffWithinAt π s x)
#align fderiv_within_const_smul fderivWithin_const_smul
/- warning: fderiv_const_smul -> fderiv_const_smul is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : R), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f y)) x) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)))
-but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (DifferentiableAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : R), Eq.{max (succ u3) (succ u2)} (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f y)) x) (HSMul.hSMul.{u1, max u2 u3, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c (fderiv.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)))
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_const_smul fderiv_const_smulβ'. -/
theorem fderiv_const_smul (h : DifferentiableAt π f x) (c : R) :
fderiv π (fun y => c β’ f y) x = c β’ fderiv π f x :=
@@ -183,10 +153,7 @@ section Add
/- warning: has_strict_fderiv_at.add -> HasStrictFDerivAt.add is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) f' g') x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) f' g') x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.add HasStrictFDerivAt.addβ'. -/
theorem HasStrictFDerivAt.add (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDerivAt g g' x) :
HasStrictFDerivAt (fun y => f y + g y) (f' + g') x :=
@@ -197,10 +164,7 @@ theorem HasStrictFDerivAt.add (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDe
#align has_strict_fderiv_at.add HasStrictFDerivAt.add
/- warning: has_fderiv_at_filter.add -> HasFDerivAtFilter.add is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) f' g') x L)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) f' g') x L)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.add HasFDerivAtFilter.addβ'. -/
theorem HasFDerivAtFilter.add (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivAtFilter g g' x L) :
HasFDerivAtFilter (fun y => f y + g y) (f' + g') x L :=
@@ -211,10 +175,7 @@ theorem HasFDerivAtFilter.add (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivA
#align has_fderiv_at_filter.add HasFDerivAtFilter.add
/- warning: has_fderiv_within_at.add -> HasFDerivWithinAt.add is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) f' g') s x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) f' g') s x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.add HasFDerivWithinAt.addβ'. -/
theorem HasFDerivWithinAt.add (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivWithinAt g g' s x) :
HasFDerivWithinAt (fun y => f y + g y) (f' + g') s x :=
@@ -222,10 +183,7 @@ theorem HasFDerivWithinAt.add (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivW
#align has_fderiv_within_at.add HasFDerivWithinAt.add
/- warning: has_fderiv_at.add -> HasFDerivAt.add is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f x) (g x)) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) f' g') x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f x) (g x)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) f' g') x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at.add HasFDerivAt.addβ'. -/
theorem HasFDerivAt.add (hf : HasFDerivAt f f' x) (hg : HasFDerivAt g g' x) :
HasFDerivAt (fun x => f x + g x) (f' + g') x :=
@@ -277,10 +235,7 @@ theorem Differentiable.add (hf : Differentiable π f) (hg : Differentiable
#align differentiable.add Differentiable.add
/- warning: fderiv_within_add -> fderivWithin_add is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) s x) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x)))
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E 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u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x)))
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_within_add fderivWithin_addβ'. -/
theorem fderivWithin_add (hxs : UniqueDiffWithinAt π s x) (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) :
@@ -289,10 +244,7 @@ theorem fderivWithin_add (hxs : UniqueDiffWithinAt π s x) (hf : Differentiabl
#align fderiv_within_add fderivWithin_add
/- warning: fderiv_add -> fderiv_add is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) x) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x)))
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) x) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x)))
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_add fderiv_addβ'. -/
theorem fderiv_add (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
fderiv π (fun y => f y + g y) x = fderiv π f x + fderiv π g x :=
@@ -434,10 +386,7 @@ theorem differentiable_add_const_iff (c : F) :
#align differentiable_add_const_iff differentiable_add_const_iff
/- warning: fderiv_within_add_const -> fderivWithin_add_const is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) s x) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x))
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) s x) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x))
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_within_add_const fderivWithin_add_constβ'. -/
theorem fderivWithin_add_const (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => f y + c) s x = fderivWithin π f s x :=
@@ -450,10 +399,7 @@ theorem fderivWithin_add_const (hxs : UniqueDiffWithinAt π s x) (c : F) :
#align fderiv_within_add_const fderivWithin_add_const
/- warning: fderiv_add_const -> fderiv_add_const is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} (c : F), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) x) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
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- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} (c : F), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u2, u2, u2} F F F (instHAdd.{u2} F (AddZeroClass.toAdd.{u2} F (AddMonoid.toAddZeroClass.{u2} F (SubNegMonoid.toAddMonoid.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4))))))) (f y) c) x) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_add_const fderiv_add_constβ'. -/
theorem fderiv_add_const (c : F) : fderiv π (fun y => f y + c) x = fderiv π f x := by
simp only [β fderivWithin_univ, fderivWithin_add_const uniqueDiffWithinAt_univ]
@@ -594,10 +540,7 @@ theorem differentiable_const_add_iff (c : F) :
#align differentiable_const_add_iff differentiable_const_add_iff
/- warning: fderiv_within_const_add -> fderivWithin_const_add is a dubious translation:
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- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y)) s x) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x))
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- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y)) s x) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x))
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_within_const_add fderivWithin_const_addβ'. -/
theorem fderivWithin_const_add (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => c + f y) s x = fderivWithin π f s x := by
@@ -605,10 +548,7 @@ theorem fderivWithin_const_add (hxs : UniqueDiffWithinAt π s x) (c : F) :
#align fderiv_within_const_add fderivWithin_const_add
/- warning: fderiv_const_add -> fderiv_const_add is a dubious translation:
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- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} (c : F), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u2, u2, u2} F F F (instHAdd.{u2} F (AddZeroClass.toAdd.{u2} F (AddMonoid.toAddZeroClass.{u2} F (SubNegMonoid.toAddMonoid.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4))))))) c (f y)) x) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_const_add fderiv_const_addβ'. -/
theorem fderiv_const_add (c : F) : fderiv π (fun y => c + f y) x = fderiv π f x := by
simp only [add_comm c, fderiv_add_const]
@@ -626,10 +566,7 @@ open BigOperators
variable {ΞΉ : Type _} {u : Finset ΞΉ} {A : ΞΉ β E β F} {A' : ΞΉ β E βL[π] F}
/- warning: has_strict_fderiv_at.sum -> HasStrictFDerivAt.sum is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x)) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x)) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u1, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.sum HasStrictFDerivAt.sumβ'. -/
theorem HasStrictFDerivAt.sum (h : β i β u, HasStrictFDerivAt (A i) (A' i) x) :
HasStrictFDerivAt (fun y => β i in u, A i y) (β i in u, A' i) x :=
@@ -640,10 +577,7 @@ theorem HasStrictFDerivAt.sum (h : β i β u, HasStrictFDerivAt (A i) (A' i) x
#align has_strict_fderiv_at.sum HasStrictFDerivAt.sum
/- warning: has_fderiv_at_filter.sum -> HasFDerivAtFilter.sum is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {L : Filter.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x L)) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x L)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {L : Filter.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x L)) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u1, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x L)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.sum HasFDerivAtFilter.sumβ'. -/
theorem HasFDerivAtFilter.sum (h : β i β u, HasFDerivAtFilter (A i) (A' i) x L) :
HasFDerivAtFilter (fun y => β i in u, A i y) (β i in u, A' i) x L :=
@@ -654,10 +588,7 @@ theorem HasFDerivAtFilter.sum (h : β i β u, HasFDerivAtFilter (A i) (A' i) x
#align has_fderiv_at_filter.sum HasFDerivAtFilter.sum
/- warning: has_fderiv_within_at.sum -> HasFDerivWithinAt.sum is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) s x)) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) s x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) s x)) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u1, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) s x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.sum HasFDerivWithinAt.sumβ'. -/
theorem HasFDerivWithinAt.sum (h : β i β u, HasFDerivWithinAt (A i) (A' i) s x) :
HasFDerivWithinAt (fun y => β i in u, A i y) (β i in u, A' i) s x :=
@@ -665,10 +596,7 @@ theorem HasFDerivWithinAt.sum (h : β i β u, HasFDerivWithinAt (A i) (A' i) s
#align has_fderiv_within_at.sum HasFDerivWithinAt.sum
/- warning: has_fderiv_at.sum -> HasFDerivAt.sum is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x)) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x)) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u1, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at.sum HasFDerivAt.sumβ'. -/
theorem HasFDerivAt.sum (h : β i β u, HasFDerivAt (A i) (A' i) x) :
HasFDerivAt (fun y => β i in u, A i y) (β i in u, A' i) x :=
@@ -722,10 +650,7 @@ theorem Differentiable.sum (h : β i β u, Differentiable π (A i)) :
#align differentiable.sum Differentiable.sum
/- warning: fderiv_within_sum -> fderivWithin_sum is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) s x) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)))
-but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u4, u1} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {s : Set.{u3} E} {ΞΉ : Type.{u2}} {u : Finset.{u2} ΞΉ} {A : ΞΉ -> E -> F}, (UniqueDiffWithinAt.{u4, u3} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) s x) -> (forall (i : ΞΉ), (Membership.mem.{u2, u2} ΞΉ (Finset.{u2} ΞΉ) (Finset.instMembershipFinset.{u2} ΞΉ) i u) -> (DifferentiableWithinAt.{u4, u3, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)) -> (Eq.{max (succ u3) (succ u1)} (ContinuousLinearMap.{u4, u4, u3, u1} 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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u1} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u4, u3, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u2} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) s x) (Finset.sum.{max u1 u3, u2} (ContinuousLinearMap.{u4, u4, u3, u1} 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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u1} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u4, u4, u3, u1} 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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u1} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => fderivWithin.{u4, u3, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)))
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_within_sum fderivWithin_sumβ'. -/
theorem fderivWithin_sum (hxs : UniqueDiffWithinAt π s x)
(h : β i β u, DifferentiableWithinAt π (A i) s x) :
@@ -734,10 +659,7 @@ theorem fderivWithin_sum (hxs : UniqueDiffWithinAt π s x)
#align fderiv_within_sum fderivWithin_sum
/- warning: fderiv_sum -> fderiv_sum is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) x) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)))
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) x) (Finset.sum.{max u1 u2, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)))
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_sum fderiv_sumβ'. -/
theorem fderiv_sum (h : β i β u, DifferentiableAt π (A i) x) :
fderiv π (fun y => β i in u, A i y) x = β i in u, fderiv π (A i) x :=
@@ -752,10 +674,7 @@ section Neg
/- warning: has_strict_fderiv_at.neg -> HasStrictFDerivAt.neg is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.neg HasStrictFDerivAt.negβ'. -/
theorem HasStrictFDerivAt.neg (h : HasStrictFDerivAt f f' x) :
HasStrictFDerivAt (fun x => -f x) (-f') x :=
@@ -763,10 +682,7 @@ theorem HasStrictFDerivAt.neg (h : HasStrictFDerivAt f f' x) :
#align has_strict_fderiv_at.neg HasStrictFDerivAt.neg
/- warning: has_fderiv_at_filter.neg -> HasFDerivAtFilter.neg is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x L)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x L)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.neg HasFDerivAtFilter.negβ'. -/
theorem HasFDerivAtFilter.neg (h : HasFDerivAtFilter f f' x L) :
HasFDerivAtFilter (fun x => -f x) (-f') x L :=
@@ -774,10 +690,7 @@ theorem HasFDerivAtFilter.neg (h : HasFDerivAtFilter f f' x L) :
#align has_fderiv_at_filter.neg HasFDerivAtFilter.neg
/- warning: has_fderiv_within_at.neg -> HasFDerivWithinAt.neg is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') s x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') s x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.neg HasFDerivWithinAt.negβ'. -/
theorem HasFDerivWithinAt.neg (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt (fun x => -f x) (-f') s x :=
@@ -785,10 +698,7 @@ theorem HasFDerivWithinAt.neg (h : HasFDerivWithinAt f f' s x) :
#align has_fderiv_within_at.neg HasFDerivWithinAt.neg
/- warning: has_fderiv_at.neg -> HasFDerivAt.neg is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at.neg HasFDerivAt.negβ'. -/
theorem HasFDerivAt.neg (h : HasFDerivAt f f' x) : HasFDerivAt (fun x => -f x) (-f') x :=
h.neg
@@ -881,10 +791,7 @@ theorem differentiable_neg_iff : (Differentiable π fun y => -f y) β Differe
#align differentiable_neg_iff differentiable_neg_iff
/- warning: fderiv_within_neg -> fderivWithin_neg is a dubious translation:
-lean 3 declaration is
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(NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F 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+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_within_neg fderivWithin_negβ'. -/
theorem fderivWithin_neg (hxs : UniqueDiffWithinAt π s x) :
fderivWithin π (fun y => -f y) s x = -fderivWithin π f s x :=
@@ -897,10 +804,7 @@ theorem fderivWithin_neg (hxs : UniqueDiffWithinAt π s x) :
#align fderiv_within_neg fderivWithin_neg
/- warning: fderiv_neg -> fderiv_neg is a dubious translation:
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- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E}, Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π 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_inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f y)) x) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x))
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π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u2} F (NegZeroClass.toNeg.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)))))) (f y)) x) (Neg.neg.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u3, u2} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) 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_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x))
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_neg fderiv_negβ'. -/
@[simp]
theorem fderiv_neg : fderiv π (fun y => -f y) x = -fderiv π f x := by
@@ -915,10 +819,7 @@ section Sub
/- warning: has_strict_fderiv_at.sub -> HasStrictFDerivAt.sub is a dubious translation:
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- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) f' g') x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) f' g') x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.sub HasStrictFDerivAt.subβ'. -/
theorem HasStrictFDerivAt.sub (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDerivAt g g' x) :
HasStrictFDerivAt (fun x => f x - g x) (f' - g') x := by
@@ -926,10 +827,7 @@ theorem HasStrictFDerivAt.sub (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDe
#align has_strict_fderiv_at.sub HasStrictFDerivAt.sub
/- warning: has_fderiv_at_filter.sub -> HasFDerivAtFilter.sub is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) f' g') x L)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) f' g') x L)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.sub HasFDerivAtFilter.subβ'. -/
theorem HasFDerivAtFilter.sub (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivAtFilter g g' x L) :
HasFDerivAtFilter (fun x => f x - g x) (f' - g') x L := by
@@ -937,10 +835,7 @@ theorem HasFDerivAtFilter.sub (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivA
#align has_fderiv_at_filter.sub HasFDerivAtFilter.sub
/- warning: has_fderiv_within_at.sub -> HasFDerivWithinAt.sub is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) f' g') s x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) f' g') s x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.sub HasFDerivWithinAt.subβ'. -/
theorem HasFDerivWithinAt.sub (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivWithinAt g g' s x) :
HasFDerivWithinAt (fun x => f x - g x) (f' - g') s x :=
@@ -948,10 +843,7 @@ theorem HasFDerivWithinAt.sub (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivW
#align has_fderiv_within_at.sub HasFDerivWithinAt.sub
/- warning: has_fderiv_at.sub -> HasFDerivAt.sub is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) f' g') x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) f' g') x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at.sub HasFDerivAt.subβ'. -/
theorem HasFDerivAt.sub (hf : HasFDerivAt f f' x) (hg : HasFDerivAt g g' x) :
HasFDerivAt (fun x => f x - g x) (f' - g') x :=
@@ -1003,10 +895,7 @@ theorem Differentiable.sub (hf : Differentiable π f) (hg : Differentiable
#align differentiable.sub Differentiable.sub
/- warning: fderiv_within_sub -> fderivWithin_sub is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) (g y)) s x) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x)))
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) (g y)) s x) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x)))
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_within_sub fderivWithin_subβ'. -/
theorem fderivWithin_sub (hxs : UniqueDiffWithinAt π s x) (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) :
@@ -1015,10 +904,7 @@ theorem fderivWithin_sub (hxs : UniqueDiffWithinAt π s x) (hf : Differentiabl
#align fderiv_within_sub fderivWithin_sub
/- warning: fderiv_sub -> fderiv_sub is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) (g y)) x) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x)))
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) (g y)) x) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x)))
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_sub fderiv_subβ'. -/
theorem fderiv_sub (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
fderiv π (fun y => f y - g y) x = fderiv π f x - fderiv π g x :=
@@ -1160,10 +1046,7 @@ theorem differentiable_sub_const_iff (c : F) :
#align differentiable_sub_const_iff differentiable_sub_const_iff
/- warning: fderiv_within_sub_const -> fderivWithin_sub_const is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_within_sub_const fderivWithin_sub_constβ'. -/
theorem fderivWithin_sub_const (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => f y - c) s x = fderivWithin π f s x := by
@@ -1171,20 +1054,14 @@ theorem fderivWithin_sub_const (hxs : UniqueDiffWithinAt π s x) (c : F) :
#align fderiv_within_sub_const fderivWithin_sub_const
/- warning: fderiv_sub_const -> fderiv_sub_const is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_sub_const fderiv_sub_constβ'. -/
theorem fderiv_sub_const (c : F) : fderiv π (fun y => f y - c) x = fderiv π f x := by
simp only [sub_eq_add_neg, fderiv_add_const]
#align fderiv_sub_const fderiv_sub_const
/- warning: has_strict_fderiv_at.const_sub -> HasStrictFDerivAt.const_sub is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.const_sub HasStrictFDerivAt.const_subβ'. -/
theorem HasStrictFDerivAt.const_sub (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun x => c - f x) (-f') x := by
@@ -1192,10 +1069,7 @@ theorem HasStrictFDerivAt.const_sub (hf : HasStrictFDerivAt f f' x) (c : F) :
#align has_strict_fderiv_at.const_sub HasStrictFDerivAt.const_sub
/- warning: has_fderiv_at_filter.const_sub -> HasFDerivAtFilter.const_sub is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x L)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x L)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.const_sub HasFDerivAtFilter.const_subβ'. -/
theorem HasFDerivAtFilter.const_sub (hf : HasFDerivAtFilter f f' x L) (c : F) :
HasFDerivAtFilter (fun x => c - f x) (-f') x L := by
@@ -1203,10 +1077,7 @@ theorem HasFDerivAtFilter.const_sub (hf : HasFDerivAtFilter f f' x L) (c : F) :
#align has_fderiv_at_filter.const_sub HasFDerivAtFilter.const_sub
/- warning: has_fderiv_within_at.const_sub -> HasFDerivWithinAt.const_sub is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') s x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') s x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.const_sub HasFDerivWithinAt.const_subβ'. -/
theorem HasFDerivWithinAt.const_sub (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun x => c - f x) (-f') s x :=
@@ -1214,10 +1085,7 @@ theorem HasFDerivWithinAt.const_sub (hf : HasFDerivWithinAt f f' s x) (c : F) :
#align has_fderiv_within_at.const_sub HasFDerivWithinAt.const_sub
/- warning: has_fderiv_at.const_sub -> HasFDerivAt.const_sub is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at.const_sub HasFDerivAt.const_subβ'. -/
theorem HasFDerivAt.const_sub (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => c - f x) (-f') x :=
@@ -1312,10 +1180,7 @@ theorem differentiable_const_sub_iff (c : F) :
#align differentiable_const_sub_iff differentiable_const_sub_iff
/- warning: fderiv_within_const_sub -> fderivWithin_const_sub is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y)) s x) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f y)) s x) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_within_const_sub fderivWithin_const_subβ'. -/
theorem fderivWithin_const_sub (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => c - f y) s x = -fderivWithin π f s x := by
@@ -1323,10 +1188,7 @@ theorem fderivWithin_const_sub (hxs : UniqueDiffWithinAt π s x) (c : F) :
#align fderiv_within_const_sub fderivWithin_const_sub
/- warning: fderiv_const_sub -> fderiv_const_sub is a dubious translation:
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_inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y)) x) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x))
-but is expected to have type
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} (c : F), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u2, u2, u2} F F F (instHSub.{u2} F (SubNegMonoid.toSub.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4))))) c (f y)) x) (Neg.neg.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u3, u2} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) 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_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x))
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_const_sub fderiv_const_subβ'. -/
theorem fderiv_const_sub (c : F) : fderiv π (fun y => c - f y) x = -fderiv π f x := by
simp only [β fderivWithin_univ, fderivWithin_const_sub uniqueDiffWithinAt_univ]
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -70,7 +70,7 @@ variable {R : Type _} [Semiring R] [Module R F] [SMulCommClass π R F] [Contin
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : R), HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f x)) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c f') x)
but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {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_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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)} {x : E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (HasStrictFDerivAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : R), HasStrictFDerivAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f x)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c f') x)
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {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_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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)} {x : E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (HasStrictFDerivAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : R), HasStrictFDerivAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f x)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c f') x)
Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.const_smul HasStrictFDerivAt.const_smulβ'. -/
theorem HasStrictFDerivAt.const_smul (h : HasStrictFDerivAt f f' x) (c : R) :
HasStrictFDerivAt (fun x => c β’ f x) (c β’ f') x :=
@@ -81,7 +81,7 @@ theorem HasStrictFDerivAt.const_smul (h : HasStrictFDerivAt f f' x) (c : R) :
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : R), HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f x)) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c f') x L)
but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {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_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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)} {x : E} {L : Filter.{u3} E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (HasFDerivAtFilter.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : R), HasFDerivAtFilter.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f x)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c f') x L)
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {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_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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)} {x : E} {L : Filter.{u3} E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (HasFDerivAtFilter.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : R), HasFDerivAtFilter.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f x)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c f') x L)
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.const_smul HasFDerivAtFilter.const_smulβ'. -/
theorem HasFDerivAtFilter.const_smul (h : HasFDerivAtFilter f f' x L) (c : R) :
HasFDerivAtFilter (fun x => c β’ f x) (c β’ f') x L :=
@@ -92,7 +92,7 @@ theorem HasFDerivAtFilter.const_smul (h : HasFDerivAtFilter f f' x L) (c : R) :
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : R), HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f x)) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c f') s x)
but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {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_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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)} {x : E} {s : Set.{u3} E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (HasFDerivWithinAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : R), HasFDerivWithinAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f x)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c f') s x)
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {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_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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)} {x : E} {s : Set.{u3} E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (HasFDerivWithinAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : R), HasFDerivWithinAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f x)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c f') s x)
Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.const_smul HasFDerivWithinAt.const_smulβ'. -/
theorem HasFDerivWithinAt.const_smul (h : HasFDerivWithinAt f f' s x) (c : R) :
HasFDerivWithinAt (fun x => c β’ f x) (c β’ f') s x :=
@@ -103,7 +103,7 @@ theorem HasFDerivWithinAt.const_smul (h : HasFDerivWithinAt f f' s x) (c : R) :
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : R), HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f x)) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c f') x)
but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {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_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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)} {x : E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (HasFDerivAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : R), HasFDerivAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f x)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c f') x)
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {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_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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)} {x : E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (HasFDerivAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : R), HasFDerivAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f x)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c f') x)
Case conversion may be inaccurate. Consider using '#align has_fderiv_at.const_smul HasFDerivAt.const_smulβ'. -/
theorem HasFDerivAt.const_smul (h : HasFDerivAt f f' x) (c : R) :
HasFDerivAt (fun x => c β’ f x) (c β’ f') x :=
@@ -156,7 +156,7 @@ theorem Differentiable.const_smul (h : Differentiable π f) (c : R) :
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : R), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f y)) s x) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u3} E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (UniqueDiffWithinAt.{u4, u3} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : R), Eq.{max (succ u3) (succ u2)} (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderivWithin.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f y)) s x) (HSMul.hSMul.{u1, max u2 u3, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c (fderivWithin.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u3} E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (UniqueDiffWithinAt.{u4, u3} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : R), Eq.{max (succ u3) (succ u2)} (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderivWithin.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f y)) s x) (HSMul.hSMul.{u1, max u2 u3, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E 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(PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c (fderivWithin.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
Case conversion may be inaccurate. Consider using '#align fderiv_within_const_smul fderivWithin_const_smulβ'. -/
theorem fderivWithin_const_smul (hxs : UniqueDiffWithinAt π s x)
(h : DifferentiableWithinAt π f s x) (c : R) :
@@ -168,7 +168,7 @@ theorem fderivWithin_const_smul (hxs : UniqueDiffWithinAt π s x)
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : R), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f y)) x) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)))
but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (DifferentiableAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : R), Eq.{max (succ u3) (succ u2)} (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f y)) x) (HSMul.hSMul.{u1, max u2 u3, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c (fderiv.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)))
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (DifferentiableAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : R), Eq.{max (succ u3) (succ u2)} (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f y)) x) (HSMul.hSMul.{u1, max u2 u3, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c (fderiv.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)))
Case conversion may be inaccurate. Consider using '#align fderiv_const_smul fderiv_const_smulβ'. -/
theorem fderiv_const_smul (h : DifferentiableAt π f x) (c : R) :
fderiv π (fun y => c β’ f y) x = c β’ fderiv π f x :=
@@ -186,7 +186,7 @@ section Add
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) f' g') x)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) f' g') x)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) f' g') x)
Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.add HasStrictFDerivAt.addβ'. -/
theorem HasStrictFDerivAt.add (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDerivAt g g' x) :
HasStrictFDerivAt (fun y => f y + g y) (f' + g') x :=
@@ -200,7 +200,7 @@ theorem HasStrictFDerivAt.add (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDe
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) f' g') x L)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) f' g') x L)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) f' g') x L)
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.add HasFDerivAtFilter.addβ'. -/
theorem HasFDerivAtFilter.add (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivAtFilter g g' x L) :
HasFDerivAtFilter (fun y => f y + g y) (f' + g') x L :=
@@ -214,7 +214,7 @@ theorem HasFDerivAtFilter.add (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivA
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) f' g') s x)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) f' g') s x)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) f' g') s x)
Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.add HasFDerivWithinAt.addβ'. -/
theorem HasFDerivWithinAt.add (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivWithinAt g g' s x) :
HasFDerivWithinAt (fun y => f y + g y) (f' + g') s x :=
@@ -225,7 +225,7 @@ theorem HasFDerivWithinAt.add (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivW
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f x) (g x)) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) f' g') x)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f x) (g x)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) f' g') x)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f x) (g x)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) f' g') x)
Case conversion may be inaccurate. Consider using '#align has_fderiv_at.add HasFDerivAt.addβ'. -/
theorem HasFDerivAt.add (hf : HasFDerivAt f f' x) (hg : HasFDerivAt g g' x) :
HasFDerivAt (fun x => f x + g x) (f' + g') x :=
@@ -280,7 +280,7 @@ theorem Differentiable.add (hf : Differentiable π f) (hg : Differentiable
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) s x) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x)))
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) s x) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x)))
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) s x) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x)))
Case conversion may be inaccurate. Consider using '#align fderiv_within_add fderivWithin_addβ'. -/
theorem fderivWithin_add (hxs : UniqueDiffWithinAt π s x) (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) :
@@ -292,7 +292,7 @@ theorem fderivWithin_add (hxs : UniqueDiffWithinAt π s x) (hf : Differentiabl
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) x) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x)))
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) x) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x)))
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) x) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x)))
Case conversion may be inaccurate. Consider using '#align fderiv_add fderiv_addβ'. -/
theorem fderiv_add (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
fderiv π (fun y => f y + g y) x = fderiv π f x + fderiv π g x :=
@@ -629,7 +629,7 @@ variable {ΞΉ : Type _} {u : Finset ΞΉ} {A : ΞΉ β E β F} {A' : ΞΉ β E βL[
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x)) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x)) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u1, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x)) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u1, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x)
Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.sum HasStrictFDerivAt.sumβ'. -/
theorem HasStrictFDerivAt.sum (h : β i β u, HasStrictFDerivAt (A i) (A' i) x) :
HasStrictFDerivAt (fun y => β i in u, A i y) (β i in u, A' i) x :=
@@ -643,7 +643,7 @@ theorem HasStrictFDerivAt.sum (h : β i β u, HasStrictFDerivAt (A i) (A' i) x
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {L : Filter.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x L)) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x L)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {L : Filter.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x L)) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u1, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x L)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {L : Filter.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x L)) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u1, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x L)
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.sum HasFDerivAtFilter.sumβ'. -/
theorem HasFDerivAtFilter.sum (h : β i β u, HasFDerivAtFilter (A i) (A' i) x L) :
HasFDerivAtFilter (fun y => β i in u, A i y) (β i in u, A' i) x L :=
@@ -657,7 +657,7 @@ theorem HasFDerivAtFilter.sum (h : β i β u, HasFDerivAtFilter (A i) (A' i) x
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) s x)) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) s x)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) s x)) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u1, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) s x)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) s x)) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u1, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) s x)
Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.sum HasFDerivWithinAt.sumβ'. -/
theorem HasFDerivWithinAt.sum (h : β i β u, HasFDerivWithinAt (A i) (A' i) s x) :
HasFDerivWithinAt (fun y => β i in u, A i y) (β i in u, A' i) s x :=
@@ -668,7 +668,7 @@ theorem HasFDerivWithinAt.sum (h : β i β u, HasFDerivWithinAt (A i) (A' i) s
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x)) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x)) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u1, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x)) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u1, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x)
Case conversion may be inaccurate. Consider using '#align has_fderiv_at.sum HasFDerivAt.sumβ'. -/
theorem HasFDerivAt.sum (h : β i β u, HasFDerivAt (A i) (A' i) x) :
HasFDerivAt (fun y => β i in u, A i y) (β i in u, A' i) x :=
@@ -725,7 +725,7 @@ theorem Differentiable.sum (h : β i β u, Differentiable π (A i)) :
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) s x) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)))
but is expected to have type
- forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u4, u1} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {s : Set.{u3} E} {ΞΉ : Type.{u2}} {u : Finset.{u2} ΞΉ} {A : ΞΉ -> E -> F}, (UniqueDiffWithinAt.{u4, u3} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) s x) -> (forall (i : ΞΉ), (Membership.mem.{u2, u2} ΞΉ (Finset.{u2} ΞΉ) (Finset.instMembershipFinset.{u2} ΞΉ) i u) -> (DifferentiableWithinAt.{u4, u3, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)) -> (Eq.{max (succ u3) (succ u1)} (ContinuousLinearMap.{u4, u4, u3, u1} 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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u1} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u4, u3, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u2} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) s x) (Finset.sum.{max u1 u3, u2} (ContinuousLinearMap.{u4, u4, u3, u1} 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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u1} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u4, u4, u3, u1} 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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u1} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => fderivWithin.{u4, u3, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)))
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u4, u1} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {s : Set.{u3} E} {ΞΉ : Type.{u2}} {u : Finset.{u2} ΞΉ} {A : ΞΉ -> E -> F}, (UniqueDiffWithinAt.{u4, u3} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) s x) -> (forall (i : ΞΉ), (Membership.mem.{u2, u2} ΞΉ (Finset.{u2} ΞΉ) (Finset.instMembershipFinset.{u2} ΞΉ) i u) -> (DifferentiableWithinAt.{u4, u3, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)) -> (Eq.{max (succ u3) (succ u1)} (ContinuousLinearMap.{u4, u4, u3, u1} 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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u1} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u4, u3, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u2} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) s x) (Finset.sum.{max u1 u3, u2} (ContinuousLinearMap.{u4, u4, u3, u1} 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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u1} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u4, u4, u3, u1} 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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u1} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => fderivWithin.{u4, u3, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)))
Case conversion may be inaccurate. Consider using '#align fderiv_within_sum fderivWithin_sumβ'. -/
theorem fderivWithin_sum (hxs : UniqueDiffWithinAt π s x)
(h : β i β u, DifferentiableWithinAt π (A i) s x) :
@@ -737,7 +737,7 @@ theorem fderivWithin_sum (hxs : UniqueDiffWithinAt π s x)
lean 3 declaration is
forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) x) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)))
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) x) (Finset.sum.{max u1 u2, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)))
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) x) (Finset.sum.{max u1 u2, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)))
Case conversion may be inaccurate. Consider using '#align fderiv_sum fderiv_sumβ'. -/
theorem fderiv_sum (h : β i β u, DifferentiableAt π (A i) x) :
fderiv π (fun y => β i in u, A i y) x = β i in u, fderiv π (A i) x :=
@@ -753,9 +753,9 @@ section Neg
/- warning: has_strict_fderiv_at.neg -> HasStrictFDerivAt.neg is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x)
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x)
Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.neg HasStrictFDerivAt.negβ'. -/
theorem HasStrictFDerivAt.neg (h : HasStrictFDerivAt f f' x) :
HasStrictFDerivAt (fun x => -f x) (-f') x :=
@@ -764,9 +764,9 @@ theorem HasStrictFDerivAt.neg (h : HasStrictFDerivAt f f' x) :
/- warning: has_fderiv_at_filter.neg -> HasFDerivAtFilter.neg is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x L)
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x L)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x L)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x L)
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.neg HasFDerivAtFilter.negβ'. -/
theorem HasFDerivAtFilter.neg (h : HasFDerivAtFilter f f' x L) :
HasFDerivAtFilter (fun x => -f x) (-f') x L :=
@@ -775,9 +775,9 @@ theorem HasFDerivAtFilter.neg (h : HasFDerivAtFilter f f' x L) :
/- warning: has_fderiv_within_at.neg -> HasFDerivWithinAt.neg is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') s x)
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') s x)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') s x)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') s x)
Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.neg HasFDerivWithinAt.negβ'. -/
theorem HasFDerivWithinAt.neg (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt (fun x => -f x) (-f') s x :=
@@ -786,9 +786,9 @@ theorem HasFDerivWithinAt.neg (h : HasFDerivWithinAt f f' s x) :
/- warning: has_fderiv_at.neg -> HasFDerivAt.neg is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x)
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x)
Case conversion may be inaccurate. Consider using '#align has_fderiv_at.neg HasFDerivAt.negβ'. -/
theorem HasFDerivAt.neg (h : HasFDerivAt f f' x) : HasFDerivAt (fun x => -f x) (-f') x :=
h.neg
@@ -882,9 +882,9 @@ theorem differentiable_neg_iff : (Differentiable π fun y => -f y) β Differe
/- warning: fderiv_within_neg -> fderivWithin_neg is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f y)) s x) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f y)) s x) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f y)) s x) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f y)) s x) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
Case conversion may be inaccurate. Consider using '#align fderiv_within_neg fderivWithin_negβ'. -/
theorem fderivWithin_neg (hxs : UniqueDiffWithinAt π s x) :
fderivWithin π (fun y => -f y) s x = -fderivWithin π f s x :=
@@ -898,9 +898,9 @@ theorem fderivWithin_neg (hxs : UniqueDiffWithinAt π s x) :
/- warning: fderiv_neg -> fderiv_neg is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E}, Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f y)) x) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x))
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E}, Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f y)) x) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x))
but is expected to have type
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E}, Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u2} F (NegZeroClass.toNeg.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)))))) (f y)) x) (Neg.neg.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u3, u2} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) 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_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x))
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E}, Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u2} F (NegZeroClass.toNeg.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)))))) (f y)) x) (Neg.neg.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u3, u2} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) 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_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x))
Case conversion may be inaccurate. Consider using '#align fderiv_neg fderiv_negβ'. -/
@[simp]
theorem fderiv_neg : fderiv π (fun y => -f y) x = -fderiv π f x := by
@@ -916,9 +916,9 @@ section Sub
/- warning: has_strict_fderiv_at.sub -> HasStrictFDerivAt.sub is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) f' g') x)
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) f' g') x)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) f' g') x)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) f' g') x)
Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.sub HasStrictFDerivAt.subβ'. -/
theorem HasStrictFDerivAt.sub (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDerivAt g g' x) :
HasStrictFDerivAt (fun x => f x - g x) (f' - g') x := by
@@ -927,9 +927,9 @@ theorem HasStrictFDerivAt.sub (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDe
/- warning: has_fderiv_at_filter.sub -> HasFDerivAtFilter.sub is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) f' g') x L)
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) f' g') x L)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) f' g') x L)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) f' g') x L)
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.sub HasFDerivAtFilter.subβ'. -/
theorem HasFDerivAtFilter.sub (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivAtFilter g g' x L) :
HasFDerivAtFilter (fun x => f x - g x) (f' - g') x L := by
@@ -938,9 +938,9 @@ theorem HasFDerivAtFilter.sub (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivA
/- warning: has_fderiv_within_at.sub -> HasFDerivWithinAt.sub is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) f' g') s x)
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) f' g') s x)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) f' g') s x)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) f' g') s x)
Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.sub HasFDerivWithinAt.subβ'. -/
theorem HasFDerivWithinAt.sub (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivWithinAt g g' s x) :
HasFDerivWithinAt (fun x => f x - g x) (f' - g') s x :=
@@ -949,9 +949,9 @@ theorem HasFDerivWithinAt.sub (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivW
/- warning: has_fderiv_at.sub -> HasFDerivAt.sub is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) f' g') x)
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) f' g') x)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) f' g') x)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) f' g') x)
Case conversion may be inaccurate. Consider using '#align has_fderiv_at.sub HasFDerivAt.subβ'. -/
theorem HasFDerivAt.sub (hf : HasFDerivAt f f' x) (hg : HasFDerivAt g g' x) :
HasFDerivAt (fun x => f x - g x) (f' - g') x :=
@@ -1004,9 +1004,9 @@ theorem Differentiable.sub (hf : Differentiable π f) (hg : Differentiable
/- warning: fderiv_within_sub -> fderivWithin_sub is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) (g y)) s x) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x)))
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) (g y)) s x) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x)))
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) (g y)) s x) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x)))
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) (g y)) s x) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x)))
Case conversion may be inaccurate. Consider using '#align fderiv_within_sub fderivWithin_subβ'. -/
theorem fderivWithin_sub (hxs : UniqueDiffWithinAt π s x) (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) :
@@ -1016,9 +1016,9 @@ theorem fderivWithin_sub (hxs : UniqueDiffWithinAt π s x) (hf : Differentiabl
/- warning: fderiv_sub -> fderiv_sub is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) (g y)) x) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x)))
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) (g y)) x) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x)))
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) (g y)) x) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x)))
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) (g y)) x) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x)))
Case conversion may be inaccurate. Consider using '#align fderiv_sub fderiv_subβ'. -/
theorem fderiv_sub (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
fderiv π (fun y => f y - g y) x = fderiv π f x - fderiv π g x :=
@@ -1182,9 +1182,9 @@ theorem fderiv_sub_const (c : F) : fderiv π (fun y => f y - c) x = fderiv
/- warning: has_strict_fderiv_at.const_sub -> HasStrictFDerivAt.const_sub is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x)
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x)
Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.const_sub HasStrictFDerivAt.const_subβ'. -/
theorem HasStrictFDerivAt.const_sub (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun x => c - f x) (-f') x := by
@@ -1193,9 +1193,9 @@ theorem HasStrictFDerivAt.const_sub (hf : HasStrictFDerivAt f f' x) (c : F) :
/- warning: has_fderiv_at_filter.const_sub -> HasFDerivAtFilter.const_sub is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x L)
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x L)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x L)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x L)
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.const_sub HasFDerivAtFilter.const_subβ'. -/
theorem HasFDerivAtFilter.const_sub (hf : HasFDerivAtFilter f f' x L) (c : F) :
HasFDerivAtFilter (fun x => c - f x) (-f') x L := by
@@ -1204,9 +1204,9 @@ theorem HasFDerivAtFilter.const_sub (hf : HasFDerivAtFilter f f' x L) (c : F) :
/- warning: has_fderiv_within_at.const_sub -> HasFDerivWithinAt.const_sub is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') s x)
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') s x)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') s x)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') s x)
Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.const_sub HasFDerivWithinAt.const_subβ'. -/
theorem HasFDerivWithinAt.const_sub (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun x => c - f x) (-f') s x :=
@@ -1215,9 +1215,9 @@ theorem HasFDerivWithinAt.const_sub (hf : HasFDerivWithinAt f f' s x) (c : F) :
/- warning: has_fderiv_at.const_sub -> HasFDerivAt.const_sub is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x)
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x)
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x)
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x)
Case conversion may be inaccurate. Consider using '#align has_fderiv_at.const_sub HasFDerivAt.const_subβ'. -/
theorem HasFDerivAt.const_sub (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => c - f x) (-f') x :=
@@ -1313,9 +1313,9 @@ theorem differentiable_const_sub_iff (c : F) :
/- warning: fderiv_within_const_sub -> fderivWithin_const_sub is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y)) s x) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y)) s x) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f y)) s x) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f y)) s x) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
Case conversion may be inaccurate. Consider using '#align fderiv_within_const_sub fderivWithin_const_subβ'. -/
theorem fderivWithin_const_sub (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => c - f y) s x = -fderivWithin π f s x := by
@@ -1324,9 +1324,9 @@ theorem fderivWithin_const_sub (hxs : UniqueDiffWithinAt π s x) (c : F) :
/- warning: fderiv_const_sub -> fderiv_const_sub is a dubious translation:
lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} (c : F), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y)) x) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x))
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} (c : F), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y)) x) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x))
but is expected to have type
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} (c : F), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u2, u2, u2} F F F (instHSub.{u2} F (SubNegMonoid.toSub.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4))))) c (f y)) x) (Neg.neg.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u3, u2} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) 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_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x))
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} (c : F), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u2, u2, u2} F F F (instHSub.{u2} F (SubNegMonoid.toSub.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4))))) c (f y)) x) (Neg.neg.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u3, u2} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) 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_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.toTopologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x))
Case conversion may be inaccurate. Consider using '#align fderiv_const_sub fderiv_const_subβ'. -/
theorem fderiv_const_sub (c : F) : fderiv π (fun y => c - f y) x = -fderiv π f x := by
simp only [β fderivWithin_univ, fderivWithin_const_sub uniqueDiffWithinAt_univ]
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.add
-! 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.
-/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.Calculus.Fderiv.Comp
/-!
# Additive operations on derivatives
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
For detailed documentation of the FrΓ©chet derivative,
see the module docstring of `analysis/calculus/fderiv/basic.lean`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -63,50 +63,110 @@ variable {R : Type _} [Semiring R] [Module R F] [SMulCommClass π R F] [Contin
/-! ### Derivative of a function multiplied by a constant -/
+/- warning: has_strict_fderiv_at.const_smul -> HasStrictFDerivAt.const_smul is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : R), HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f x)) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c f') x)
+but is expected to have type
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {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_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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)} {x : E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (HasStrictFDerivAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : R), HasStrictFDerivAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f x)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c f') x)
+Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.const_smul HasStrictFDerivAt.const_smulβ'. -/
theorem HasStrictFDerivAt.const_smul (h : HasStrictFDerivAt f f' x) (c : R) :
HasStrictFDerivAt (fun x => c β’ f x) (c β’ f') x :=
(c β’ (1 : F βL[π] F)).HasStrictFDerivAt.comp x h
#align has_strict_fderiv_at.const_smul HasStrictFDerivAt.const_smul
+/- warning: has_fderiv_at_filter.const_smul -> HasFDerivAtFilter.const_smul is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : R), HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f x)) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c f') x L)
+but is expected to have type
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {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_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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)} {x : E} {L : Filter.{u3} E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (HasFDerivAtFilter.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : R), HasFDerivAtFilter.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f x)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c f') x L)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.const_smul HasFDerivAtFilter.const_smulβ'. -/
theorem HasFDerivAtFilter.const_smul (h : HasFDerivAtFilter f f' x L) (c : R) :
HasFDerivAtFilter (fun x => c β’ f x) (c β’ f') x L :=
(c β’ (1 : F βL[π] F)).HasFDerivAtFilter.comp x h tendsto_map
#align has_fderiv_at_filter.const_smul HasFDerivAtFilter.const_smul
+/- warning: has_fderiv_within_at.const_smul -> HasFDerivWithinAt.const_smul is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : R), HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f x)) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c f') s x)
+but is expected to have type
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {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_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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)} {x : E} {s : Set.{u3} E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (HasFDerivWithinAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : R), HasFDerivWithinAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f x)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c f') s x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.const_smul HasFDerivWithinAt.const_smulβ'. -/
theorem HasFDerivWithinAt.const_smul (h : HasFDerivWithinAt f f' s x) (c : R) :
HasFDerivWithinAt (fun x => c β’ f x) (c β’ f') s x :=
h.const_smul c
#align has_fderiv_within_at.const_smul HasFDerivWithinAt.const_smul
+/- warning: has_fderiv_at.const_smul -> HasFDerivAt.const_smul is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : R), HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f x)) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c f') x)
+but is expected to have type
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {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_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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)} {x : E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (HasFDerivAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : R), HasFDerivAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f x)) (HSMul.hSMul.{u1, max u3 u2, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c f') x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at.const_smul HasFDerivAt.const_smulβ'. -/
theorem HasFDerivAt.const_smul (h : HasFDerivAt f f' x) (c : R) :
HasFDerivAt (fun x => c β’ f x) (c β’ f') x :=
h.const_smul c
#align has_fderiv_at.const_smul HasFDerivAt.const_smul
+/- warning: differentiable_within_at.const_smul -> DifferentiableWithinAt.const_smul is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : R), DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f y)) s x)
+but is expected to have type
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u3} E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (DifferentiableWithinAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : R), DifferentiableWithinAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f y)) s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at.const_smul DifferentiableWithinAt.const_smulβ'. -/
theorem DifferentiableWithinAt.const_smul (h : DifferentiableWithinAt π f s x) (c : R) :
DifferentiableWithinAt π (fun y => c β’ f y) s x :=
(h.HasFDerivWithinAt.const_smul c).DifferentiableWithinAt
#align differentiable_within_at.const_smul DifferentiableWithinAt.const_smul
+/- warning: differentiable_at.const_smul -> DifferentiableAt.const_smul is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : R), DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f y)) x)
+but is expected to have type
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (DifferentiableAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : R), DifferentiableAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f y)) x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at.const_smul DifferentiableAt.const_smulβ'. -/
theorem DifferentiableAt.const_smul (h : DifferentiableAt π f x) (c : R) :
DifferentiableAt π (fun y => c β’ f y) x :=
(h.HasFDerivAt.const_smul c).DifferentiableAt
#align differentiable_at.const_smul DifferentiableAt.const_smul
+/- warning: differentiable_on.const_smul -> DifferentiableOn.const_smul is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {s : Set.{u2} E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (forall (c : R), DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f y)) s)
+but is expected to have type
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {s : Set.{u3} E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (DifferentiableOn.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (forall (c : R), DifferentiableOn.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f y)) s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on.const_smul DifferentiableOn.const_smulβ'. -/
theorem DifferentiableOn.const_smul (h : DifferentiableOn π f s) (c : R) :
DifferentiableOn π (fun y => c β’ f y) s := fun x hx => (h x hx).const_smul c
#align differentiable_on.const_smul DifferentiableOn.const_smul
+/- warning: differentiable.const_smul -> Differentiable.const_smul is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (forall (c : R), Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f y)))
+but is expected to have type
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (Differentiable.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (forall (c : R), Differentiable.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f y)))
+Case conversion may be inaccurate. Consider using '#align differentiable.const_smul Differentiable.const_smulβ'. -/
theorem Differentiable.const_smul (h : Differentiable π f) (c : R) :
Differentiable π fun y => c β’ f y := fun x => (h x).const_smul c
#align differentiable.const_smul Differentiable.const_smul
+/- warning: fderiv_within_const_smul -> fderivWithin_const_smul is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : R), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f y)) s x) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
+but is expected to have type
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u3} E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (UniqueDiffWithinAt.{u4, u3} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : R), Eq.{max (succ u3) (succ u2)} (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderivWithin.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f y)) s x) (HSMul.hSMul.{u1, max u2 u3, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c (fderivWithin.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
+Case conversion may be inaccurate. Consider using '#align fderiv_within_const_smul fderivWithin_const_smulβ'. -/
theorem fderivWithin_const_smul (hxs : UniqueDiffWithinAt π s x)
(h : DifferentiableWithinAt π f s x) (c : R) :
fderivWithin π (fun y => c β’ f y) s x = c β’ fderivWithin π f s x :=
(h.HasFDerivWithinAt.const_smul c).fderivWithin hxs
#align fderiv_within_const_smul fderivWithin_const_smul
+/- warning: fderiv_const_smul -> fderiv_const_smul is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {R : Type.{u4}} [_inst_10 : Semiring.{u4} R] [_inst_11 : Module.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))] [_inst_12 : SMulCommClass.{u1, u4, u3} π R F (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u4, u3} R F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11))))], (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : R), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => SMul.smul.{u4, u3} R F (SMulZeroClass.toHasSmul.{u4, u3} R F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (SMulWithZero.toSmulZeroClass.{u4, u3} R F (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (MulActionWithZero.toSMulWithZero.{u4, u3} R F (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4))))) (Module.toMulActionWithZero.{u4, u3} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) _inst_11)))) c (f y)) x) (SMul.smul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (SMulZeroClass.toHasSmul.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (SMulWithZero.toSmulZeroClass.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (MulZeroClass.toHasZero.{u4} R (MulZeroOneClass.toMulZeroClass.{u4} R (MonoidWithZero.toMulZeroOneClass.{u4} R (Semiring.toMonoidWithZero.{u4} R _inst_10)))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u4} R _inst_10) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))))) (Module.toMulActionWithZero.{u4, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (ContinuousLinearMap.module.{u1, u1, u4, u2, u3} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))))))) c (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)))
+but is expected to have type
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} {R : Type.{u1}} [_inst_10 : Semiring.{u1} R] [_inst_11 : Module.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4))] [_inst_12 : SMulCommClass.{u4, u1, u2} π R F (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_4)))))) (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_4)))))) (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_4)))))) (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_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5))))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))] [_inst_13 : ContinuousConstSMul.{u1, u2} R F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))], (DifferentiableAt.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : R), Eq.{max (succ u3) (succ u2)} (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSMul.hSMul.{u1, u2, u2} R F F (instHSMul.{u1, u2} R F (SMulZeroClass.toSMul.{u1, u2} R 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_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} R F (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (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_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R F (Semiring.toMonoidWithZero.{u1} R _inst_10) (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_4)))))) (Module.toMulActionWithZero.{u1, u2} R F _inst_10 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) _inst_11))))) c (f y)) x) (HSMul.hSMul.{u1, max u2 u3, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (instHSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulZeroClass.toSMul.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_10)) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Semiring.toMonoidWithZero.{u1} R _inst_10) (ContinuousLinearMap.zero.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (Module.toMulActionWithZero.{u1, max u3 u2} R (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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) _inst_10 (ContinuousLinearMap.addCommMonoid.{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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousLinearMap.module.{u4, u4, u1, u3, u2} π π R (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))))) _inst_10 E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) _inst_11 _inst_12 _inst_13 (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))))))) (TopologicalAddGroup.toContinuousAdd.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))))))))) c (fderiv.{u4, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)))
+Case conversion may be inaccurate. Consider using '#align fderiv_const_smul fderiv_const_smulβ'. -/
theorem fderiv_const_smul (h : DifferentiableAt π f x) (c : R) :
fderiv π (fun y => c β’ f y) x = c β’ fderiv π f x :=
(h.HasFDerivAt.const_smul c).fderiv
@@ -119,6 +179,12 @@ section Add
/-! ### Derivative of the sum of two functions -/
+/- warning: has_strict_fderiv_at.add -> HasStrictFDerivAt.add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) f' g') x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) f' g') x)
+Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.add HasStrictFDerivAt.addβ'. -/
theorem HasStrictFDerivAt.add (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDerivAt g g' x) :
HasStrictFDerivAt (fun y => f y + g y) (f' + g') x :=
(hf.add hg).congr_left fun y =>
@@ -127,6 +193,12 @@ theorem HasStrictFDerivAt.add (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDe
abel
#align has_strict_fderiv_at.add HasStrictFDerivAt.add
+/- warning: has_fderiv_at_filter.add -> HasFDerivAtFilter.add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) f' g') x L)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) f' g') x L)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.add HasFDerivAtFilter.addβ'. -/
theorem HasFDerivAtFilter.add (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivAtFilter g g' x L) :
HasFDerivAtFilter (fun y => f y + g y) (f' + g') x L :=
(hf.add hg).congr_left fun _ =>
@@ -135,109 +207,235 @@ theorem HasFDerivAtFilter.add (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivA
abel
#align has_fderiv_at_filter.add HasFDerivAtFilter.add
+/- warning: has_fderiv_within_at.add -> HasFDerivWithinAt.add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) f' g') s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) f' g') s x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.add HasFDerivWithinAt.addβ'. -/
theorem HasFDerivWithinAt.add (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivWithinAt g g' s x) :
HasFDerivWithinAt (fun y => f y + g y) (f' + g') s x :=
hf.add hg
#align has_fderiv_within_at.add HasFDerivWithinAt.add
+/- warning: has_fderiv_at.add -> HasFDerivAt.add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f x) (g x)) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) f' g') x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f x) (g x)) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) f' g') x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at.add HasFDerivAt.addβ'. -/
theorem HasFDerivAt.add (hf : HasFDerivAt f f' x) (hg : HasFDerivAt g g' x) :
HasFDerivAt (fun x => f x + g x) (f' + g') x :=
hf.add hg
#align has_fderiv_at.add HasFDerivAt.add
+/- warning: differentiable_within_at.add -> DifferentiableWithinAt.add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at.add DifferentiableWithinAt.addβ'. -/
theorem DifferentiableWithinAt.add (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) : DifferentiableWithinAt π (fun y => f y + g y) s x :=
(hf.HasFDerivWithinAt.add hg.HasFDerivWithinAt).DifferentiableWithinAt
#align differentiable_within_at.add DifferentiableWithinAt.add
+/- warning: differentiable_at.add -> DifferentiableAt.add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at.add DifferentiableAt.addβ'. -/
@[simp]
theorem DifferentiableAt.add (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
DifferentiableAt π (fun y => f y + g y) x :=
(hf.HasFDerivAt.add hg.HasFDerivAt).DifferentiableAt
#align differentiable_at.add DifferentiableAt.add
+/- warning: differentiable_on.add -> DifferentiableOn.add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) s)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on.add DifferentiableOn.addβ'. -/
theorem DifferentiableOn.add (hf : DifferentiableOn π f s) (hg : DifferentiableOn π g s) :
DifferentiableOn π (fun y => f y + g y) s := fun x hx => (hf x hx).add (hg x hx)
#align differentiable_on.add DifferentiableOn.add
+/- warning: differentiable.add -> Differentiable.add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F}, (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F}, (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)))
+Case conversion may be inaccurate. Consider using '#align differentiable.add Differentiable.addβ'. -/
@[simp]
theorem Differentiable.add (hf : Differentiable π f) (hg : Differentiable π g) :
Differentiable π fun y => f y + g y := fun x => (hf x).add (hg x)
#align differentiable.add Differentiable.add
+/- warning: fderiv_within_add -> fderivWithin_add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) s x) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x)))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) s x) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x)))
+Case conversion may be inaccurate. Consider using '#align fderiv_within_add fderivWithin_addβ'. -/
theorem fderivWithin_add (hxs : UniqueDiffWithinAt π s x) (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) :
fderivWithin π (fun y => f y + g y) s x = fderivWithin π f s x + fderivWithin π g s x :=
(hf.HasFDerivWithinAt.add hg.HasFDerivWithinAt).fderivWithin hxs
#align fderiv_within_add fderivWithin_add
+/- warning: fderiv_add -> fderiv_add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) (g y)) x) (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHAdd.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))))) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x)))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) (g y)) x) (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHAdd.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.add.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))))) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x)))
+Case conversion may be inaccurate. Consider using '#align fderiv_add fderiv_addβ'. -/
theorem fderiv_add (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
fderiv π (fun y => f y + g y) x = fderiv π f x + fderiv π g x :=
(hf.HasFDerivAt.add hg.HasFDerivAt).fderiv
#align fderiv_add fderiv_add
+/- warning: has_strict_fderiv_at.add_const -> HasStrictFDerivAt.add_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) f' x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) f' x)
+Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.add_const HasStrictFDerivAt.add_constβ'. -/
theorem HasStrictFDerivAt.add_const (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun y => f y + c) f' x :=
add_zero f' βΈ hf.add (hasStrictFDerivAt_const _ _)
#align has_strict_fderiv_at.add_const HasStrictFDerivAt.add_const
+/- warning: has_fderiv_at_filter.add_const -> HasFDerivAtFilter.add_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) f' x L)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) f' x L)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.add_const HasFDerivAtFilter.add_constβ'. -/
theorem HasFDerivAtFilter.add_const (hf : HasFDerivAtFilter f f' x L) (c : F) :
HasFDerivAtFilter (fun y => f y + c) f' x L :=
add_zero f' βΈ hf.add (hasFDerivAtFilter_const _ _ _)
#align has_fderiv_at_filter.add_const HasFDerivAtFilter.add_const
+/- warning: has_fderiv_within_at.add_const -> HasFDerivWithinAt.add_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) f' s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) f' s x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.add_const HasFDerivWithinAt.add_constβ'. -/
theorem HasFDerivWithinAt.add_const (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun y => f y + c) f' s x :=
hf.AddConst c
#align has_fderiv_within_at.add_const HasFDerivWithinAt.add_const
+/- warning: has_fderiv_at.add_const -> HasFDerivAt.add_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f x) c) f' x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f x) c) f' x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at.add_const HasFDerivAt.add_constβ'. -/
theorem HasFDerivAt.add_const (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => f x + c) f' x :=
hf.AddConst c
#align has_fderiv_at.add_const HasFDerivAt.add_const
+/- warning: differentiable_within_at.add_const -> DifferentiableWithinAt.add_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : F), DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : F), DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at.add_const DifferentiableWithinAt.add_constβ'. -/
theorem DifferentiableWithinAt.add_const (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => f y + c) s x :=
(hf.HasFDerivWithinAt.AddConst c).DifferentiableWithinAt
#align differentiable_within_at.add_const DifferentiableWithinAt.add_const
+/- warning: differentiable_within_at_add_const_iff -> differentiableWithinAt_add_const_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (c : F), Iff (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) s x) (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (c : F), Iff (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) s x) (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at_add_const_iff differentiableWithinAt_add_const_iffβ'. -/
@[simp]
theorem differentiableWithinAt_add_const_iff (c : F) :
DifferentiableWithinAt π (fun y => f y + c) s x β DifferentiableWithinAt π f s x :=
β¨fun h => by simpa using h.add_const (-c), fun h => h.AddConst cβ©
#align differentiable_within_at_add_const_iff differentiableWithinAt_add_const_iff
+/- warning: differentiable_at.add_const -> DifferentiableAt.add_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : F), DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : F), DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at.add_const DifferentiableAt.add_constβ'. -/
theorem DifferentiableAt.add_const (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => f y + c) x :=
(hf.HasFDerivAt.AddConst c).DifferentiableAt
#align differentiable_at.add_const DifferentiableAt.add_const
+/- warning: differentiable_at_add_const_iff -> differentiableAt_add_const_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} (c : F), Iff (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) x) (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} (c : F), Iff (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) x) (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at_add_const_iff differentiableAt_add_const_iffβ'. -/
@[simp]
theorem differentiableAt_add_const_iff (c : F) :
DifferentiableAt π (fun y => f y + c) x β DifferentiableAt π f x :=
β¨fun h => by simpa using h.add_const (-c), fun h => h.AddConst cβ©
#align differentiable_at_add_const_iff differentiableAt_add_const_iff
+/- warning: differentiable_on.add_const -> DifferentiableOn.add_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (forall (c : F), DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) s)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (forall (c : F), DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on.add_const DifferentiableOn.add_constβ'. -/
theorem DifferentiableOn.add_const (hf : DifferentiableOn π f s) (c : F) :
DifferentiableOn π (fun y => f y + c) s := fun x hx => (hf x hx).AddConst c
#align differentiable_on.add_const DifferentiableOn.add_const
+/- warning: differentiable_on_add_const_iff -> differentiableOn_add_const_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {s : Set.{u2} E} (c : F), Iff (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) s) (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {s : Set.{u2} E} (c : F), Iff (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) s) (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on_add_const_iff differentiableOn_add_const_iffβ'. -/
@[simp]
theorem differentiableOn_add_const_iff (c : F) :
DifferentiableOn π (fun y => f y + c) s β DifferentiableOn π f s :=
β¨fun h => by simpa using h.add_const (-c), fun h => h.AddConst cβ©
#align differentiable_on_add_const_iff differentiableOn_add_const_iff
+/- warning: differentiable.add_const -> Differentiable.add_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F}, (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (forall (c : F), Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F}, (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (forall (c : F), Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c))
+Case conversion may be inaccurate. Consider using '#align differentiable.add_const Differentiable.add_constβ'. -/
theorem Differentiable.add_const (hf : Differentiable π f) (c : F) :
Differentiable π fun y => f y + c := fun x => (hf x).AddConst c
#align differentiable.add_const Differentiable.add_const
+/- warning: differentiable_add_const_iff -> differentiable_add_const_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} (c : F), Iff (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c)) (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} (c : F), Iff (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c)) (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
+Case conversion may be inaccurate. Consider using '#align differentiable_add_const_iff differentiable_add_const_iffβ'. -/
@[simp]
theorem differentiable_add_const_iff (c : F) :
(Differentiable π fun y => f y + c) β Differentiable π f :=
β¨fun h => by simpa using h.add_const (-c), fun h => h.AddConst cβ©
#align differentiable_add_const_iff differentiable_add_const_iff
+/- warning: fderiv_within_add_const -> fderivWithin_add_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) s x) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) (f y) c) s x) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x))
+Case conversion may be inaccurate. Consider using '#align fderiv_within_add_const fderivWithin_add_constβ'. -/
theorem fderivWithin_add_const (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => f y + c) s x = fderivWithin π f s x :=
if hf : DifferentiableWithinAt π f s x then (hf.HasFDerivWithinAt.AddConst c).fderivWithin hxs
@@ -248,77 +446,167 @@ theorem fderivWithin_add_const (hxs : UniqueDiffWithinAt π s x) (c : F) :
simpa
#align fderiv_within_add_const fderivWithin_add_const
+/- warning: fderiv_add_const -> fderiv_add_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} (c : F), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) (f y) c) x) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+but is expected to have type
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} (c : F), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u2, u2, u2} F F F (instHAdd.{u2} F (AddZeroClass.toAdd.{u2} F (AddMonoid.toAddZeroClass.{u2} F (SubNegMonoid.toAddMonoid.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4))))))) (f y) c) x) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+Case conversion may be inaccurate. Consider using '#align fderiv_add_const fderiv_add_constβ'. -/
theorem fderiv_add_const (c : F) : fderiv π (fun y => f y + c) x = fderiv π f x := by
simp only [β fderivWithin_univ, fderivWithin_add_const uniqueDiffWithinAt_univ]
#align fderiv_add_const fderiv_add_const
+/- warning: has_strict_fderiv_at.const_add -> HasStrictFDerivAt.const_add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y)) f' x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y)) f' x)
+Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.const_add HasStrictFDerivAt.const_addβ'. -/
theorem HasStrictFDerivAt.const_add (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun y => c + f y) f' x :=
zero_add f' βΈ (hasStrictFDerivAt_const _ _).add hf
#align has_strict_fderiv_at.const_add HasStrictFDerivAt.const_add
+/- warning: has_fderiv_at_filter.const_add -> HasFDerivAtFilter.const_add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y)) f' x L)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y)) f' x L)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.const_add HasFDerivAtFilter.const_addβ'. -/
theorem HasFDerivAtFilter.const_add (hf : HasFDerivAtFilter f f' x L) (c : F) :
HasFDerivAtFilter (fun y => c + f y) f' x L :=
zero_add f' βΈ (hasFDerivAtFilter_const _ _ _).add hf
#align has_fderiv_at_filter.const_add HasFDerivAtFilter.const_add
+/- warning: has_fderiv_within_at.const_add -> HasFDerivWithinAt.const_add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y)) f' s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y)) f' s x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.const_add HasFDerivWithinAt.const_addβ'. -/
theorem HasFDerivWithinAt.const_add (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun y => c + f y) f' s x :=
hf.const_add c
#align has_fderiv_within_at.const_add HasFDerivWithinAt.const_add
+/- warning: has_fderiv_at.const_add -> HasFDerivAt.const_add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f x)) f' x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f x)) f' x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at.const_add HasFDerivAt.const_addβ'. -/
theorem HasFDerivAt.const_add (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => c + f x) f' x :=
hf.const_add c
#align has_fderiv_at.const_add HasFDerivAt.const_add
+/- warning: differentiable_within_at.const_add -> DifferentiableWithinAt.const_add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : F), DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y)) s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : F), DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y)) s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at.const_add DifferentiableWithinAt.const_addβ'. -/
theorem DifferentiableWithinAt.const_add (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => c + f y) s x :=
(hf.HasFDerivWithinAt.const_add c).DifferentiableWithinAt
#align differentiable_within_at.const_add DifferentiableWithinAt.const_add
+/- warning: differentiable_within_at_const_add_iff -> differentiableWithinAt_const_add_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (c : F), Iff (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y)) s x) (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (c : F), Iff (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y)) s x) (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at_const_add_iff differentiableWithinAt_const_add_iffβ'. -/
@[simp]
theorem differentiableWithinAt_const_add_iff (c : F) :
DifferentiableWithinAt π (fun y => c + f y) s x β DifferentiableWithinAt π f s x :=
β¨fun h => by simpa using h.const_add (-c), fun h => h.const_add cβ©
#align differentiable_within_at_const_add_iff differentiableWithinAt_const_add_iff
+/- warning: differentiable_at.const_add -> DifferentiableAt.const_add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : F), DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y)) x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : F), DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y)) x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at.const_add DifferentiableAt.const_addβ'. -/
theorem DifferentiableAt.const_add (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => c + f y) x :=
(hf.HasFDerivAt.const_add c).DifferentiableAt
#align differentiable_at.const_add DifferentiableAt.const_add
+/- warning: differentiable_at_const_add_iff -> differentiableAt_const_add_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} (c : F), Iff (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y)) x) (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} (c : F), Iff (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y)) x) (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at_const_add_iff differentiableAt_const_add_iffβ'. -/
@[simp]
theorem differentiableAt_const_add_iff (c : F) :
DifferentiableAt π (fun y => c + f y) x β DifferentiableAt π f x :=
β¨fun h => by simpa using h.const_add (-c), fun h => h.const_add cβ©
#align differentiable_at_const_add_iff differentiableAt_const_add_iff
+/- warning: differentiable_on.const_add -> DifferentiableOn.const_add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (forall (c : F), DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y)) s)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (forall (c : F), DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y)) s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on.const_add DifferentiableOn.const_addβ'. -/
theorem DifferentiableOn.const_add (hf : DifferentiableOn π f s) (c : F) :
DifferentiableOn π (fun y => c + f y) s := fun x hx => (hf x hx).const_add c
#align differentiable_on.const_add DifferentiableOn.const_add
+/- warning: differentiable_on_const_add_iff -> differentiableOn_const_add_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {s : Set.{u2} E} (c : F), Iff (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y)) s) (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {s : Set.{u2} E} (c : F), Iff (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y)) s) (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on_const_add_iff differentiableOn_const_add_iffβ'. -/
@[simp]
theorem differentiableOn_const_add_iff (c : F) :
DifferentiableOn π (fun y => c + f y) s β DifferentiableOn π f s :=
β¨fun h => by simpa using h.const_add (-c), fun h => h.const_add cβ©
#align differentiable_on_const_add_iff differentiableOn_const_add_iff
+/- warning: differentiable.const_add -> Differentiable.const_add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F}, (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (forall (c : F), Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y)))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F}, (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (forall (c : F), Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y)))
+Case conversion may be inaccurate. Consider using '#align differentiable.const_add Differentiable.const_addβ'. -/
theorem Differentiable.const_add (hf : Differentiable π f) (c : F) :
Differentiable π fun y => c + f y := fun x => (hf x).const_add c
#align differentiable.const_add Differentiable.const_add
+/- warning: differentiable_const_add_iff -> differentiable_const_add_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} (c : F), Iff (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y))) (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} (c : F), Iff (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y))) (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
+Case conversion may be inaccurate. Consider using '#align differentiable_const_add_iff differentiable_const_add_iffβ'. -/
@[simp]
theorem differentiable_const_add_iff (c : F) :
(Differentiable π fun y => c + f y) β Differentiable π f :=
β¨fun h => by simpa using h.const_add (-c), fun h => h.const_add cβ©
#align differentiable_const_add_iff differentiable_const_add_iff
+/- warning: fderiv_within_const_add -> fderivWithin_const_add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y)) s x) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u1, u1, u1} F F F (instHAdd.{u1} F (AddZeroClass.toAdd.{u1} F (AddMonoid.toAddZeroClass.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))))) c (f y)) s x) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x))
+Case conversion may be inaccurate. Consider using '#align fderiv_within_const_add fderivWithin_const_addβ'. -/
theorem fderivWithin_const_add (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => c + f y) s x = fderivWithin π f s x := by
simpa only [add_comm] using fderivWithin_add_const hxs c
#align fderiv_within_const_add fderivWithin_const_add
+/- warning: fderiv_const_add -> fderiv_const_add is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} (c : F), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u3, u3, u3} F F F (instHAdd.{u3} F (AddZeroClass.toHasAdd.{u3} F (AddMonoid.toAddZeroClass.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))))) c (f y)) x) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+but is expected to have type
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} (c : F), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HAdd.hAdd.{u2, u2, u2} F F F (instHAdd.{u2} F (AddZeroClass.toAdd.{u2} F (AddMonoid.toAddZeroClass.{u2} F (SubNegMonoid.toAddMonoid.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4))))))) c (f y)) x) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+Case conversion may be inaccurate. Consider using '#align fderiv_const_add fderiv_const_addβ'. -/
theorem fderiv_const_add (c : F) : fderiv π (fun y => c + f y) x = fderiv π f x := by
simp only [add_comm c, fderiv_add_const]
#align fderiv_const_add fderiv_const_add
@@ -334,6 +622,12 @@ open BigOperators
variable {ΞΉ : Type _} {u : Finset ΞΉ} {A : ΞΉ β E β F} {A' : ΞΉ β E βL[π] F}
+/- warning: has_strict_fderiv_at.sum -> HasStrictFDerivAt.sum is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x)) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x)) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u1, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x)
+Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.sum HasStrictFDerivAt.sumβ'. -/
theorem HasStrictFDerivAt.sum (h : β i β u, HasStrictFDerivAt (A i) (A' i) x) :
HasStrictFDerivAt (fun y => β i in u, A i y) (β i in u, A' i) x :=
by
@@ -342,6 +636,12 @@ theorem HasStrictFDerivAt.sum (h : β i β u, HasStrictFDerivAt (A i) (A' i) x
simp [Finset.sum_sub_distrib, ContinuousLinearMap.sum_apply]
#align has_strict_fderiv_at.sum HasStrictFDerivAt.sum
+/- warning: has_fderiv_at_filter.sum -> HasFDerivAtFilter.sum is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {L : Filter.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x L)) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x L)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {L : Filter.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x L)) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u1, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x L)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.sum HasFDerivAtFilter.sumβ'. -/
theorem HasFDerivAtFilter.sum (h : β i β u, HasFDerivAtFilter (A i) (A' i) x L) :
HasFDerivAtFilter (fun y => β i in u, A i y) (β i in u, A' i) x L :=
by
@@ -350,44 +650,92 @@ theorem HasFDerivAtFilter.sum (h : β i β u, HasFDerivAtFilter (A i) (A' i) x
simp [ContinuousLinearMap.sum_apply]
#align has_fderiv_at_filter.sum HasFDerivAtFilter.sum
+/- warning: has_fderiv_within_at.sum -> HasFDerivWithinAt.sum is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) s x)) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) s x)) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u1, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) s x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.sum HasFDerivWithinAt.sumβ'. -/
theorem HasFDerivWithinAt.sum (h : β i β u, HasFDerivWithinAt (A i) (A' i) s x) :
HasFDerivWithinAt (fun y => β i in u, A i y) (β i in u, A' i) s x :=
HasFDerivAtFilter.sum h
#align has_fderiv_within_at.sum HasFDerivWithinAt.sum
+/- warning: has_fderiv_at.sum -> HasFDerivAt.sum is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x)) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F} {A' : ΞΉ -> (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5))}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) (A' i) x)) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) (Finset.sum.{max u2 u1, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => A' i)) x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at.sum HasFDerivAt.sumβ'. -/
theorem HasFDerivAt.sum (h : β i β u, HasFDerivAt (A i) (A' i) x) :
HasFDerivAt (fun y => β i in u, A i y) (β i in u, A' i) x :=
HasFDerivAtFilter.sum h
#align has_fderiv_at.sum HasFDerivAt.sum
+/- warning: differentiable_within_at.sum -> DifferentiableWithinAt.sum is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at.sum DifferentiableWithinAt.sumβ'. -/
theorem DifferentiableWithinAt.sum (h : β i β u, DifferentiableWithinAt π (A i) s x) :
DifferentiableWithinAt π (fun y => β i in u, A i y) s x :=
HasFDerivWithinAt.differentiableWithinAt <|
HasFDerivWithinAt.sum fun i hi => (h i hi).HasFDerivWithinAt
#align differentiable_within_at.sum DifferentiableWithinAt.sum
+/- warning: differentiable_at.sum -> DifferentiableAt.sum is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at.sum DifferentiableAt.sumβ'. -/
@[simp]
theorem DifferentiableAt.sum (h : β i β u, DifferentiableAt π (A i) x) :
DifferentiableAt π (fun y => β i in u, A i y) x :=
HasFDerivAt.differentiableAt <| HasFDerivAt.sum fun i hi => (h i hi).HasFDerivAt
#align differentiable_at.sum DifferentiableAt.sum
+/- warning: differentiable_on.sum -> DifferentiableOn.sum is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s)) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) s)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s)) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on.sum DifferentiableOn.sumβ'. -/
theorem DifferentiableOn.sum (h : β i β u, DifferentiableOn π (A i) s) :
DifferentiableOn π (fun y => β i in u, A i y) s := fun x hx =>
DifferentiableWithinAt.sum fun i hi => h i hi x hx
#align differentiable_on.sum DifferentiableOn.sum
+/- warning: differentiable.sum -> Differentiable.sum is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i))) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i))) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)))
+Case conversion may be inaccurate. Consider using '#align differentiable.sum Differentiable.sumβ'. -/
@[simp]
theorem Differentiable.sum (h : β i β u, Differentiable π (A i)) :
Differentiable π fun y => β i in u, A i y := fun x => DifferentiableAt.sum fun i hi => h i hi x
#align differentiable.sum Differentiable.sum
+/- warning: fderiv_within_sum -> fderivWithin_sum is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {s : Set.{u2} E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) s x) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)))
+but is expected to have type
+ forall {π : Type.{u4}} [_inst_1 : NontriviallyNormedField.{u4} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u4, u1} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {s : Set.{u3} E} {ΞΉ : Type.{u2}} {u : Finset.{u2} ΞΉ} {A : ΞΉ -> E -> F}, (UniqueDiffWithinAt.{u4, u3} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) s x) -> (forall (i : ΞΉ), (Membership.mem.{u2, u2} ΞΉ (Finset.{u2} ΞΉ) (Finset.instMembershipFinset.{u2} ΞΉ) i u) -> (DifferentiableWithinAt.{u4, u3, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)) -> (Eq.{max (succ u3) (succ u1)} (ContinuousLinearMap.{u4, u4, u3, u1} 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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u1} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u4, u3, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u2} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) s x) (Finset.sum.{max u1 u3, u2} (ContinuousLinearMap.{u4, u4, u3, u1} 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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u1} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u4, u4, u3, u1} 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_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u4, u1} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => fderivWithin.{u4, u3, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) s x)))
+Case conversion may be inaccurate. Consider using '#align fderiv_within_sum fderivWithin_sumβ'. -/
theorem fderivWithin_sum (hxs : UniqueDiffWithinAt π s x)
(h : β i β u, DifferentiableWithinAt π (A i) s x) :
fderivWithin π (fun y => β i in u, A i y) s x = β i in u, fderivWithin π (A i) s x :=
(HasFDerivWithinAt.sum fun i hi => (h i hi).HasFDerivWithinAt).fderivWithin hxs
#align fderiv_within_sum fderivWithin_sum
+/- warning: fderiv_sum -> fderiv_sum is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.Mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.hasMem.{u4} ΞΉ) i u) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u3, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) u (fun (i : ΞΉ) => A i y)) x) (Finset.sum.{max u2 u3, u4} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (LipschitzAdd.continuousAdd.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)) (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) u (fun (i : ΞΉ) => fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {x : E} {ΞΉ : Type.{u4}} {u : Finset.{u4} ΞΉ} {A : ΞΉ -> E -> F}, (forall (i : ΞΉ), (Membership.mem.{u4, u4} ΞΉ (Finset.{u4} ΞΉ) (Finset.instMembershipFinset.{u4} ΞΉ) i u) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Finset.sum.{u1, u4} F ΞΉ (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) u (fun (i : ΞΉ) => A i y)) x) (Finset.sum.{max u1 u2, u4} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) ΞΉ (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) u (fun (i : ΞΉ) => fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (A i) x)))
+Case conversion may be inaccurate. Consider using '#align fderiv_sum fderiv_sumβ'. -/
theorem fderiv_sum (h : β i β u, DifferentiableAt π (A i) x) :
fderiv π (fun y => β i in u, A i y) x = β i in u, fderiv π (A i) x :=
(HasFDerivAt.sum fun i hi => (h i hi).HasFDerivAt).fderiv
@@ -400,63 +748,141 @@ section Neg
/-! ### Derivative of the negative of a function -/
+/- warning: has_strict_fderiv_at.neg -> HasStrictFDerivAt.neg is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x)
+Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.neg HasStrictFDerivAt.negβ'. -/
theorem HasStrictFDerivAt.neg (h : HasStrictFDerivAt f f' x) :
HasStrictFDerivAt (fun x => -f x) (-f') x :=
(-1 : F βL[π] F).HasStrictFDerivAt.comp x h
#align has_strict_fderiv_at.neg HasStrictFDerivAt.neg
+/- warning: has_fderiv_at_filter.neg -> HasFDerivAtFilter.neg is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x L)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x L)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.neg HasFDerivAtFilter.negβ'. -/
theorem HasFDerivAtFilter.neg (h : HasFDerivAtFilter f f' x L) :
HasFDerivAtFilter (fun x => -f x) (-f') x L :=
(-1 : F βL[π] F).HasFDerivAtFilter.comp x h tendsto_map
#align has_fderiv_at_filter.neg HasFDerivAtFilter.neg
+/- warning: has_fderiv_within_at.neg -> HasFDerivWithinAt.neg is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') s x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.neg HasFDerivWithinAt.negβ'. -/
theorem HasFDerivWithinAt.neg (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt (fun x => -f x) (-f') s x :=
h.neg
#align has_fderiv_within_at.neg HasFDerivWithinAt.neg
+/- warning: has_fderiv_at.neg -> HasFDerivAt.neg is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at.neg HasFDerivAt.negβ'. -/
theorem HasFDerivAt.neg (h : HasFDerivAt f f' x) : HasFDerivAt (fun x => -f x) (-f') x :=
h.neg
#align has_fderiv_at.neg HasFDerivAt.neg
+/- warning: differentiable_within_at.neg -> DifferentiableWithinAt.neg is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f y)) s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f y)) s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at.neg DifferentiableWithinAt.negβ'. -/
theorem DifferentiableWithinAt.neg (h : DifferentiableWithinAt π f s x) :
DifferentiableWithinAt π (fun y => -f y) s x :=
h.HasFDerivWithinAt.neg.DifferentiableWithinAt
#align differentiable_within_at.neg DifferentiableWithinAt.neg
+/- warning: differentiable_within_at_neg_iff -> differentiableWithinAt_neg_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, Iff (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f y)) s x) (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, Iff (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f y)) s x) (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at_neg_iff differentiableWithinAt_neg_iffβ'. -/
@[simp]
theorem differentiableWithinAt_neg_iff :
DifferentiableWithinAt π (fun y => -f y) s x β DifferentiableWithinAt π f s x :=
β¨fun h => by simpa only [neg_neg] using h.neg, fun h => h.negβ©
#align differentiable_within_at_neg_iff differentiableWithinAt_neg_iff
+/- warning: differentiable_at.neg -> DifferentiableAt.neg is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f y)) x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f y)) x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at.neg DifferentiableAt.negβ'. -/
theorem DifferentiableAt.neg (h : DifferentiableAt π f x) : DifferentiableAt π (fun y => -f y) x :=
h.HasFDerivAt.neg.DifferentiableAt
#align differentiable_at.neg DifferentiableAt.neg
+/- warning: differentiable_at_neg_iff -> differentiableAt_neg_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E}, Iff (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f y)) x) (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E}, Iff (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f y)) x) (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at_neg_iff differentiableAt_neg_iffβ'. -/
@[simp]
theorem differentiableAt_neg_iff : DifferentiableAt π (fun y => -f y) x β DifferentiableAt π f x :=
β¨fun h => by simpa only [neg_neg] using h.neg, fun h => h.negβ©
#align differentiable_at_neg_iff differentiableAt_neg_iff
+/- warning: differentiable_on.neg -> DifferentiableOn.neg is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f y)) s)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f y)) s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on.neg DifferentiableOn.negβ'. -/
theorem DifferentiableOn.neg (h : DifferentiableOn π f s) : DifferentiableOn π (fun y => -f y) s :=
fun x hx => (h x hx).neg
#align differentiable_on.neg DifferentiableOn.neg
+/- warning: differentiable_on_neg_iff -> differentiableOn_neg_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, Iff (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f y)) s) (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, Iff (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f y)) s) (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on_neg_iff differentiableOn_neg_iffβ'. -/
@[simp]
theorem differentiableOn_neg_iff : DifferentiableOn π (fun y => -f y) s β DifferentiableOn π f s :=
β¨fun h => by simpa only [neg_neg] using h.neg, fun h => h.negβ©
#align differentiable_on_neg_iff differentiableOn_neg_iff
+/- warning: differentiable.neg -> Differentiable.neg is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F}, (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f y)))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F}, (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f y)))
+Case conversion may be inaccurate. Consider using '#align differentiable.neg Differentiable.negβ'. -/
theorem Differentiable.neg (h : Differentiable π f) : Differentiable π fun y => -f y := fun x =>
(h x).neg
#align differentiable.neg Differentiable.neg
+/- warning: differentiable_neg_iff -> differentiable_neg_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F}, Iff (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f y))) (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F}, Iff (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f y))) (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
+Case conversion may be inaccurate. Consider using '#align differentiable_neg_iff differentiable_neg_iffβ'. -/
@[simp]
theorem differentiable_neg_iff : (Differentiable π fun y => -f y) β Differentiable π f :=
β¨fun h => by simpa only [neg_neg] using h.neg, fun h => h.negβ©
#align differentiable_neg_iff differentiable_neg_iff
+/- warning: fderiv_within_neg -> fderivWithin_neg is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f y)) s x) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u1} F (NegZeroClass.toNeg.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)))))) (f y)) s x) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
+Case conversion may be inaccurate. Consider using '#align fderiv_within_neg fderivWithin_negβ'. -/
theorem fderivWithin_neg (hxs : UniqueDiffWithinAt π s x) :
fderivWithin π (fun y => -f y) s x = -fderivWithin π f s x :=
if h : DifferentiableWithinAt π f s x then h.HasFDerivWithinAt.neg.fderivWithin hxs
@@ -467,6 +893,12 @@ theorem fderivWithin_neg (hxs : UniqueDiffWithinAt π s x) :
simpa
#align fderiv_within_neg fderivWithin_neg
+/- warning: fderiv_neg -> fderiv_neg is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E}, Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u3} F (SubNegMonoid.toHasNeg.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4)))) (f y)) x) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x))
+but is expected to have type
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E}, Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => Neg.neg.{u2} F (NegZeroClass.toNeg.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)))))) (f y)) x) (Neg.neg.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u3, u2} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) 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_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x))
+Case conversion may be inaccurate. Consider using '#align fderiv_neg fderiv_negβ'. -/
@[simp]
theorem fderiv_neg : fderiv π (fun y => -f y) x = -fderiv π f x := by
simp only [β fderivWithin_univ, fderivWithin_neg uniqueDiffWithinAt_univ]
@@ -479,192 +911,420 @@ section Sub
/-! ### Derivative of the difference of two functions -/
+/- warning: has_strict_fderiv_at.sub -> HasStrictFDerivAt.sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) f' g') x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) f' g') x)
+Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.sub HasStrictFDerivAt.subβ'. -/
theorem HasStrictFDerivAt.sub (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDerivAt g g' x) :
HasStrictFDerivAt (fun x => f x - g x) (f' - g') x := by
simpa only [sub_eq_add_neg] using hf.add hg.neg
#align has_strict_fderiv_at.sub HasStrictFDerivAt.sub
+/- warning: has_fderiv_at_filter.sub -> HasFDerivAtFilter.sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) f' g') x L)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) f' g') x L)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.sub HasFDerivAtFilter.subβ'. -/
theorem HasFDerivAtFilter.sub (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivAtFilter g g' x L) :
HasFDerivAtFilter (fun x => f x - g x) (f' - g') x L := by
simpa only [sub_eq_add_neg] using hf.add hg.neg
#align has_fderiv_at_filter.sub HasFDerivAtFilter.sub
+/- warning: has_fderiv_within_at.sub -> HasFDerivWithinAt.sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) f' g') s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) f' g') s x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.sub HasFDerivWithinAt.subβ'. -/
theorem HasFDerivWithinAt.sub (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivWithinAt g g' s x) :
HasFDerivWithinAt (fun x => f x - g x) (f' - g') s x :=
hf.sub hg
#align has_fderiv_within_at.sub HasFDerivWithinAt.sub
+/- warning: has_fderiv_at.sub -> HasFDerivAt.sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) f' g') x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {g' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g g' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) (g x)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) f' g') x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at.sub HasFDerivAt.subβ'. -/
theorem HasFDerivAt.sub (hf : HasFDerivAt f f' x) (hg : HasFDerivAt g g' x) :
HasFDerivAt (fun x => f x - g x) (f' - g') x :=
hf.sub hg
#align has_fderiv_at.sub HasFDerivAt.sub
+/- warning: differentiable_within_at.sub -> DifferentiableWithinAt.sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) (g y)) s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) (g y)) s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at.sub DifferentiableWithinAt.subβ'. -/
theorem DifferentiableWithinAt.sub (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) : DifferentiableWithinAt π (fun y => f y - g y) s x :=
(hf.HasFDerivWithinAt.sub hg.HasFDerivWithinAt).DifferentiableWithinAt
#align differentiable_within_at.sub DifferentiableWithinAt.sub
+/- warning: differentiable_at.sub -> DifferentiableAt.sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) (g y)) x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) (g y)) x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at.sub DifferentiableAt.subβ'. -/
@[simp]
theorem DifferentiableAt.sub (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
DifferentiableAt π (fun y => f y - g y) x :=
(hf.HasFDerivAt.sub hg.HasFDerivAt).DifferentiableAt
#align differentiable_at.sub DifferentiableAt.sub
+/- warning: differentiable_on.sub -> DifferentiableOn.sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) (g y)) s)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) (g y)) s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on.sub DifferentiableOn.subβ'. -/
theorem DifferentiableOn.sub (hf : DifferentiableOn π f s) (hg : DifferentiableOn π g s) :
DifferentiableOn π (fun y => f y - g y) s := fun x hx => (hf x hx).sub (hg x hx)
#align differentiable_on.sub DifferentiableOn.sub
+/- warning: differentiable.sub -> Differentiable.sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F}, (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) (g y)))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F}, (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) (g y)))
+Case conversion may be inaccurate. Consider using '#align differentiable.sub Differentiable.subβ'. -/
@[simp]
theorem Differentiable.sub (hf : Differentiable π f) (hg : Differentiable π g) :
Differentiable π fun y => f y - g y := fun x => (hf x).sub (hg x)
#align differentiable.sub Differentiable.sub
+/- warning: fderiv_within_sub -> fderivWithin_sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) (g y)) s x) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x)))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) (g y)) s x) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g s x)))
+Case conversion may be inaccurate. Consider using '#align fderiv_within_sub fderivWithin_subβ'. -/
theorem fderivWithin_sub (hxs : UniqueDiffWithinAt π s x) (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) :
fderivWithin π (fun y => f y - g y) s x = fderivWithin π f s x - fderivWithin π g s x :=
(hf.HasFDerivWithinAt.sub hg.HasFDerivWithinAt).fderivWithin hxs
#align fderiv_within_sub fderivWithin_sub
+/- warning: fderiv_sub -> fderiv_sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) (g y)) x) (HSub.hSub.{max u2 u3, max u2 u3, max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (instHSub.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x)))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {g : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) (g y)) x) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (instHSub.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.sub.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 g x)))
+Case conversion may be inaccurate. Consider using '#align fderiv_sub fderiv_subβ'. -/
theorem fderiv_sub (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
fderiv π (fun y => f y - g y) x = fderiv π f x - fderiv π g x :=
(hf.HasFDerivAt.sub hg.HasFDerivAt).fderiv
#align fderiv_sub fderiv_sub
+/- warning: has_strict_fderiv_at.sub_const -> HasStrictFDerivAt.sub_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) c) f' x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) c) f' x)
+Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.sub_const HasStrictFDerivAt.sub_constβ'. -/
theorem HasStrictFDerivAt.sub_const (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun x => f x - c) f' x := by
simpa only [sub_eq_add_neg] using hf.add_const (-c)
#align has_strict_fderiv_at.sub_const HasStrictFDerivAt.sub_const
+/- warning: has_fderiv_at_filter.sub_const -> HasFDerivAtFilter.sub_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) c) f' x L)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) c) f' x L)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.sub_const HasFDerivAtFilter.sub_constβ'. -/
theorem HasFDerivAtFilter.sub_const (hf : HasFDerivAtFilter f f' x L) (c : F) :
HasFDerivAtFilter (fun x => f x - c) f' x L := by
simpa only [sub_eq_add_neg] using hf.add_const (-c)
#align has_fderiv_at_filter.sub_const HasFDerivAtFilter.sub_const
+/- warning: has_fderiv_within_at.sub_const -> HasFDerivWithinAt.sub_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) c) f' s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) c) f' s x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.sub_const HasFDerivWithinAt.sub_constβ'. -/
theorem HasFDerivWithinAt.sub_const (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun x => f x - c) f' s x :=
hf.sub_const c
#align has_fderiv_within_at.sub_const HasFDerivWithinAt.sub_const
+/- warning: has_fderiv_at.sub_const -> HasFDerivAt.sub_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f x) c) f' x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f x) c) f' x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at.sub_const HasFDerivAt.sub_constβ'. -/
theorem HasFDerivAt.sub_const (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => f x - c) f' x :=
hf.sub_const c
#align has_fderiv_at.sub_const HasFDerivAt.sub_const
+/- warning: differentiable_within_at.sub_const -> DifferentiableWithinAt.sub_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : F), DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) c) s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : F), DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) c) s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at.sub_const DifferentiableWithinAt.sub_constβ'. -/
theorem DifferentiableWithinAt.sub_const (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => f y - c) s x :=
(hf.HasFDerivWithinAt.sub_const c).DifferentiableWithinAt
#align differentiable_within_at.sub_const DifferentiableWithinAt.sub_const
+/- warning: differentiable_within_at_sub_const_iff -> differentiableWithinAt_sub_const_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (c : F), Iff (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) c) s x) (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (c : F), Iff (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) c) s x) (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at_sub_const_iff differentiableWithinAt_sub_const_iffβ'. -/
@[simp]
theorem differentiableWithinAt_sub_const_iff (c : F) :
DifferentiableWithinAt π (fun y => f y - c) s x β DifferentiableWithinAt π f s x := by
simp only [sub_eq_add_neg, differentiableWithinAt_add_const_iff]
#align differentiable_within_at_sub_const_iff differentiableWithinAt_sub_const_iff
+/- warning: differentiable_at.sub_const -> DifferentiableAt.sub_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : F), DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) c) x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : F), DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) c) x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at.sub_const DifferentiableAt.sub_constβ'. -/
theorem DifferentiableAt.sub_const (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => f y - c) x :=
(hf.HasFDerivAt.sub_const c).DifferentiableAt
#align differentiable_at.sub_const DifferentiableAt.sub_const
+/- warning: differentiable_at_sub_const_iff -> differentiableAt_sub_const_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} (c : F), Iff (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) c) x) (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} (c : F), Iff (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) c) x) (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at_sub_const_iff differentiableAt_sub_const_iffβ'. -/
@[simp]
theorem differentiableAt_sub_const_iff (c : F) :
DifferentiableAt π (fun y => f y - c) x β DifferentiableAt π f x := by
simp only [sub_eq_add_neg, differentiableAt_add_const_iff]
#align differentiable_at_sub_const_iff differentiableAt_sub_const_iff
+/- warning: differentiable_on.sub_const -> DifferentiableOn.sub_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (forall (c : F), DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) c) s)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (forall (c : F), DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) c) s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on.sub_const DifferentiableOn.sub_constβ'. -/
theorem DifferentiableOn.sub_const (hf : DifferentiableOn π f s) (c : F) :
DifferentiableOn π (fun y => f y - c) s := fun x hx => (hf x hx).sub_const c
#align differentiable_on.sub_const DifferentiableOn.sub_const
+/- warning: differentiable_on_sub_const_iff -> differentiableOn_sub_const_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {s : Set.{u2} E} (c : F), Iff (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) c) s) (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {s : Set.{u2} E} (c : F), Iff (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) c) s) (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on_sub_const_iff differentiableOn_sub_const_iffβ'. -/
@[simp]
theorem differentiableOn_sub_const_iff (c : F) :
DifferentiableOn π (fun y => f y - c) s β DifferentiableOn π f s := by
simp only [sub_eq_add_neg, differentiableOn_add_const_iff]
#align differentiable_on_sub_const_iff differentiableOn_sub_const_iff
+/- warning: differentiable.sub_const -> Differentiable.sub_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F}, (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (forall (c : F), Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) c))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F}, (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (forall (c : F), Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) c))
+Case conversion may be inaccurate. Consider using '#align differentiable.sub_const Differentiable.sub_constβ'. -/
theorem Differentiable.sub_const (hf : Differentiable π f) (c : F) :
Differentiable π fun y => f y - c := fun x => (hf x).sub_const c
#align differentiable.sub_const Differentiable.sub_const
+/- warning: differentiable_sub_const_iff -> differentiable_sub_const_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} (c : F), Iff (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) c)) (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} (c : F), Iff (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) c)) (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
+Case conversion may be inaccurate. Consider using '#align differentiable_sub_const_iff differentiable_sub_const_iffβ'. -/
@[simp]
theorem differentiable_sub_const_iff (c : F) :
(Differentiable π fun y => f y - c) β Differentiable π f := by
simp only [sub_eq_add_neg, differentiable_add_const_iff]
#align differentiable_sub_const_iff differentiable_sub_const_iff
+/- warning: fderiv_within_sub_const -> fderivWithin_sub_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) c) s x) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) (f y) c) s x) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x))
+Case conversion may be inaccurate. Consider using '#align fderiv_within_sub_const fderivWithin_sub_constβ'. -/
theorem fderivWithin_sub_const (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => f y - c) s x = fderivWithin π f s x := by
simp only [sub_eq_add_neg, fderivWithin_add_const hxs]
#align fderiv_within_sub_const fderivWithin_sub_const
+/- warning: fderiv_sub_const -> fderiv_sub_const is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} (c : F), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) (f y) c) x) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+but is expected to have type
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} (c : F), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u2, u2, u2} F F F (instHSub.{u2} F (SubNegMonoid.toSub.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4))))) (f y) c) x) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+Case conversion may be inaccurate. Consider using '#align fderiv_sub_const fderiv_sub_constβ'. -/
theorem fderiv_sub_const (c : F) : fderiv π (fun y => f y - c) x = fderiv π f x := by
simp only [sub_eq_add_neg, fderiv_add_const]
#align fderiv_sub_const fderiv_sub_const
+/- warning: has_strict_fderiv_at.const_sub -> HasStrictFDerivAt.const_sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x)
+Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.const_sub HasStrictFDerivAt.const_subβ'. -/
theorem HasStrictFDerivAt.const_sub (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun x => c - f x) (-f') x := by
simpa only [sub_eq_add_neg] using hf.neg.const_add c
#align has_strict_fderiv_at.const_sub HasStrictFDerivAt.const_sub
+/- warning: has_fderiv_at_filter.const_sub -> HasFDerivAtFilter.const_sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x L)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x L) -> (forall (c : F), HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x L)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.const_sub HasFDerivAtFilter.const_subβ'. -/
theorem HasFDerivAtFilter.const_sub (hf : HasFDerivAtFilter f f' x L) (c : F) :
HasFDerivAtFilter (fun x => c - f x) (-f') x L := by
simpa only [sub_eq_add_neg] using hf.neg.const_add c
#align has_fderiv_at_filter.const_sub HasFDerivAtFilter.const_sub
+/- warning: has_fderiv_within_at.const_sub -> HasFDerivWithinAt.const_sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' s x) -> (forall (c : F), HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') s x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.const_sub HasFDerivWithinAt.const_subβ'. -/
theorem HasFDerivWithinAt.const_sub (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun x => c - f x) (-f') s x :=
hf.const_sub c
#align has_fderiv_within_at.const_sub HasFDerivWithinAt.const_sub
+/- warning: has_fderiv_at.const_sub -> HasFDerivAt.const_sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) f') x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f f' x) -> (forall (c : F), HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (x : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f x)) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) f') x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at.const_sub HasFDerivAt.const_subβ'. -/
theorem HasFDerivAt.const_sub (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => c - f x) (-f') x :=
hf.const_sub c
#align has_fderiv_at.const_sub HasFDerivAt.const_sub
+/- warning: differentiable_within_at.const_sub -> DifferentiableWithinAt.const_sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : F), DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y)) s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) -> (forall (c : F), DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f y)) s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at.const_sub DifferentiableWithinAt.const_subβ'. -/
theorem DifferentiableWithinAt.const_sub (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => c - f y) s x :=
(hf.HasFDerivWithinAt.const_sub c).DifferentiableWithinAt
#align differentiable_within_at.const_sub DifferentiableWithinAt.const_sub
+/- warning: differentiable_within_at_const_sub_iff -> differentiableWithinAt_const_sub_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (c : F), Iff (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y)) s x) (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (c : F), Iff (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f y)) s x) (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at_const_sub_iff differentiableWithinAt_const_sub_iffβ'. -/
@[simp]
theorem differentiableWithinAt_const_sub_iff (c : F) :
DifferentiableWithinAt π (fun y => c - f y) s x β DifferentiableWithinAt π f s x := by
simp [sub_eq_add_neg]
#align differentiable_within_at_const_sub_iff differentiableWithinAt_const_sub_iff
+/- warning: differentiable_at.const_sub -> DifferentiableAt.const_sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : F), DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y)) x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) -> (forall (c : F), DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f y)) x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at.const_sub DifferentiableAt.const_subβ'. -/
theorem DifferentiableAt.const_sub (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => c - f y) x :=
(hf.HasFDerivAt.const_sub c).DifferentiableAt
#align differentiable_at.const_sub DifferentiableAt.const_sub
+/- warning: differentiable_at_const_sub_iff -> differentiableAt_const_sub_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} (c : F), Iff (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y)) x) (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} (c : F), Iff (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f y)) x) (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at_const_sub_iff differentiableAt_const_sub_iffβ'. -/
@[simp]
theorem differentiableAt_const_sub_iff (c : F) :
DifferentiableAt π (fun y => c - f y) x β DifferentiableAt π f x := by simp [sub_eq_add_neg]
#align differentiable_at_const_sub_iff differentiableAt_const_sub_iff
+/- warning: differentiable_on.const_sub -> DifferentiableOn.const_sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (forall (c : F), DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y)) s)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s) -> (forall (c : F), DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f y)) s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on.const_sub DifferentiableOn.const_subβ'. -/
theorem DifferentiableOn.const_sub (hf : DifferentiableOn π f s) (c : F) :
DifferentiableOn π (fun y => c - f y) s := fun x hx => (hf x hx).const_sub c
#align differentiable_on.const_sub DifferentiableOn.const_sub
+/- warning: differentiable_on_const_sub_iff -> differentiableOn_const_sub_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {s : Set.{u2} E} (c : F), Iff (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y)) s) (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {s : Set.{u2} E} (c : F), Iff (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f y)) s) (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on_const_sub_iff differentiableOn_const_sub_iffβ'. -/
@[simp]
theorem differentiableOn_const_sub_iff (c : F) :
DifferentiableOn π (fun y => c - f y) s β DifferentiableOn π f s := by simp [sub_eq_add_neg]
#align differentiable_on_const_sub_iff differentiableOn_const_sub_iff
+/- warning: differentiable.const_sub -> Differentiable.const_sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F}, (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (forall (c : F), Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y)))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F}, (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (forall (c : F), Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f y)))
+Case conversion may be inaccurate. Consider using '#align differentiable.const_sub Differentiable.const_subβ'. -/
theorem Differentiable.const_sub (hf : Differentiable π f) (c : F) :
Differentiable π fun y => c - f y := fun x => (hf x).const_sub c
#align differentiable.const_sub Differentiable.const_sub
+/- warning: differentiable_const_sub_iff -> differentiable_const_sub_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} (c : F), Iff (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y))) (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} (c : F), Iff (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f y))) (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
+Case conversion may be inaccurate. Consider using '#align differentiable_const_sub_iff differentiable_const_sub_iffβ'. -/
@[simp]
theorem differentiable_const_sub_iff (c : F) :
(Differentiable π fun y => c - f y) β Differentiable π f := by simp [sub_eq_add_neg]
#align differentiable_const_sub_iff differentiable_const_sub_iff
+/- warning: fderiv_within_const_sub -> fderivWithin_const_sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y)) s x) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (forall (c : F), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u1, u1, u1} F F F (instHSub.{u1} F (SubNegMonoid.toSub.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_4))))) c (f y)) s x) (Neg.neg.{max u2 u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u3, u3, u2, u1} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4))) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)))
+Case conversion may be inaccurate. Consider using '#align fderiv_within_const_sub fderivWithin_const_subβ'. -/
theorem fderivWithin_const_sub (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => c - f y) s x = -fderivWithin π f s x := by
simp only [sub_eq_add_neg, fderivWithin_const_add, fderivWithin_neg, hxs]
#align fderiv_within_const_sub fderivWithin_const_sub
+/- warning: fderiv_const_sub -> fderiv_const_sub is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} (c : F), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u3, u3, u3} F F F (instHSub.{u3} F (SubNegMonoid.toHasSub.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_4))))) c (f y)) x) (Neg.neg.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u2, u3} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4))) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x))
+but is expected to have type
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] {f : E -> F} {x : E} (c : F), Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (fun (y : E) => HSub.hSub.{u2, u2, u2} F F F (instHSub.{u2} F (SubNegMonoid.toSub.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_4))))) c (f y)) x) (Neg.neg.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (ContinuousLinearMap.neg.{u1, u1, u3, u2} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) 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_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (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))))))) (SeminormedAddCommGroup.to_topologicalAddGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4))) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x))
+Case conversion may be inaccurate. Consider using '#align fderiv_const_sub fderiv_const_subβ'. -/
theorem fderiv_const_sub (c : F) : fderiv π (fun y => c - f y) x = -fderiv π f x := by
simp only [β fderivWithin_univ, fderivWithin_const_sub uniqueDiffWithinAt_univ]
#align fderiv_const_sub fderiv_const_sub
mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952
@@ -63,34 +63,34 @@ variable {R : Type _} [Semiring R] [Module R F] [SMulCommClass π R F] [Contin
/-! ### Derivative of a function multiplied by a constant -/
-theorem HasStrictFderivAt.const_smul (h : HasStrictFderivAt f f' x) (c : R) :
- HasStrictFderivAt (fun x => c β’ f x) (c β’ f') x :=
- (c β’ (1 : F βL[π] F)).HasStrictFderivAt.comp x h
-#align has_strict_fderiv_at.const_smul HasStrictFderivAt.const_smul
-
-theorem HasFderivAtFilter.const_smul (h : HasFderivAtFilter f f' x L) (c : R) :
- HasFderivAtFilter (fun x => c β’ f x) (c β’ f') x L :=
- (c β’ (1 : F βL[π] F)).HasFderivAtFilter.comp x h tendsto_map
-#align has_fderiv_at_filter.const_smul HasFderivAtFilter.const_smul
-
-theorem HasFderivWithinAt.const_smul (h : HasFderivWithinAt f f' s x) (c : R) :
- HasFderivWithinAt (fun x => c β’ f x) (c β’ f') s x :=
+theorem HasStrictFDerivAt.const_smul (h : HasStrictFDerivAt f f' x) (c : R) :
+ HasStrictFDerivAt (fun x => c β’ f x) (c β’ f') x :=
+ (c β’ (1 : F βL[π] F)).HasStrictFDerivAt.comp x h
+#align has_strict_fderiv_at.const_smul HasStrictFDerivAt.const_smul
+
+theorem HasFDerivAtFilter.const_smul (h : HasFDerivAtFilter f f' x L) (c : R) :
+ HasFDerivAtFilter (fun x => c β’ f x) (c β’ f') x L :=
+ (c β’ (1 : F βL[π] F)).HasFDerivAtFilter.comp x h tendsto_map
+#align has_fderiv_at_filter.const_smul HasFDerivAtFilter.const_smul
+
+theorem HasFDerivWithinAt.const_smul (h : HasFDerivWithinAt f f' s x) (c : R) :
+ HasFDerivWithinAt (fun x => c β’ f x) (c β’ f') s x :=
h.const_smul c
-#align has_fderiv_within_at.const_smul HasFderivWithinAt.const_smul
+#align has_fderiv_within_at.const_smul HasFDerivWithinAt.const_smul
-theorem HasFderivAt.const_smul (h : HasFderivAt f f' x) (c : R) :
- HasFderivAt (fun x => c β’ f x) (c β’ f') x :=
+theorem HasFDerivAt.const_smul (h : HasFDerivAt f f' x) (c : R) :
+ HasFDerivAt (fun x => c β’ f x) (c β’ f') x :=
h.const_smul c
-#align has_fderiv_at.const_smul HasFderivAt.const_smul
+#align has_fderiv_at.const_smul HasFDerivAt.const_smul
theorem DifferentiableWithinAt.const_smul (h : DifferentiableWithinAt π f s x) (c : R) :
DifferentiableWithinAt π (fun y => c β’ f y) s x :=
- (h.HasFderivWithinAt.const_smul c).DifferentiableWithinAt
+ (h.HasFDerivWithinAt.const_smul c).DifferentiableWithinAt
#align differentiable_within_at.const_smul DifferentiableWithinAt.const_smul
theorem DifferentiableAt.const_smul (h : DifferentiableAt π f x) (c : R) :
DifferentiableAt π (fun y => c β’ f y) x :=
- (h.HasFderivAt.const_smul c).DifferentiableAt
+ (h.HasFDerivAt.const_smul c).DifferentiableAt
#align differentiable_at.const_smul DifferentiableAt.const_smul
theorem DifferentiableOn.const_smul (h : DifferentiableOn π f s) (c : R) :
@@ -104,12 +104,12 @@ theorem Differentiable.const_smul (h : Differentiable π f) (c : R) :
theorem fderivWithin_const_smul (hxs : UniqueDiffWithinAt π s x)
(h : DifferentiableWithinAt π f s x) (c : R) :
fderivWithin π (fun y => c β’ f y) s x = c β’ fderivWithin π f s x :=
- (h.HasFderivWithinAt.const_smul c).fderivWithin hxs
+ (h.HasFDerivWithinAt.const_smul c).fderivWithin hxs
#align fderiv_within_const_smul fderivWithin_const_smul
theorem fderiv_const_smul (h : DifferentiableAt π f x) (c : R) :
fderiv π (fun y => c β’ f y) x = c β’ fderiv π f x :=
- (h.HasFderivAt.const_smul c).fderiv
+ (h.HasFDerivAt.const_smul c).fderiv
#align fderiv_const_smul fderiv_const_smul
end ConstSmul
@@ -119,41 +119,41 @@ section Add
/-! ### Derivative of the sum of two functions -/
-theorem HasStrictFderivAt.add (hf : HasStrictFderivAt f f' x) (hg : HasStrictFderivAt g g' x) :
- HasStrictFderivAt (fun y => f y + g y) (f' + g') x :=
+theorem HasStrictFDerivAt.add (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDerivAt g g' x) :
+ HasStrictFDerivAt (fun y => f y + g y) (f' + g') x :=
(hf.add hg).congr_left fun y =>
by
simp only [LinearMap.sub_apply, LinearMap.add_apply, map_sub, map_add, add_apply]
abel
-#align has_strict_fderiv_at.add HasStrictFderivAt.add
+#align has_strict_fderiv_at.add HasStrictFDerivAt.add
-theorem HasFderivAtFilter.add (hf : HasFderivAtFilter f f' x L) (hg : HasFderivAtFilter g g' x L) :
- HasFderivAtFilter (fun y => f y + g y) (f' + g') x L :=
+theorem HasFDerivAtFilter.add (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivAtFilter g g' x L) :
+ HasFDerivAtFilter (fun y => f y + g y) (f' + g') x L :=
(hf.add hg).congr_left fun _ =>
by
simp only [LinearMap.sub_apply, LinearMap.add_apply, map_sub, map_add, add_apply]
abel
-#align has_fderiv_at_filter.add HasFderivAtFilter.add
+#align has_fderiv_at_filter.add HasFDerivAtFilter.add
-theorem HasFderivWithinAt.add (hf : HasFderivWithinAt f f' s x) (hg : HasFderivWithinAt g g' s x) :
- HasFderivWithinAt (fun y => f y + g y) (f' + g') s x :=
+theorem HasFDerivWithinAt.add (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivWithinAt g g' s x) :
+ HasFDerivWithinAt (fun y => f y + g y) (f' + g') s x :=
hf.add hg
-#align has_fderiv_within_at.add HasFderivWithinAt.add
+#align has_fderiv_within_at.add HasFDerivWithinAt.add
-theorem HasFderivAt.add (hf : HasFderivAt f f' x) (hg : HasFderivAt g g' x) :
- HasFderivAt (fun x => f x + g x) (f' + g') x :=
+theorem HasFDerivAt.add (hf : HasFDerivAt f f' x) (hg : HasFDerivAt g g' x) :
+ HasFDerivAt (fun x => f x + g x) (f' + g') x :=
hf.add hg
-#align has_fderiv_at.add HasFderivAt.add
+#align has_fderiv_at.add HasFDerivAt.add
theorem DifferentiableWithinAt.add (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) : DifferentiableWithinAt π (fun y => f y + g y) s x :=
- (hf.HasFderivWithinAt.add hg.HasFderivWithinAt).DifferentiableWithinAt
+ (hf.HasFDerivWithinAt.add hg.HasFDerivWithinAt).DifferentiableWithinAt
#align differentiable_within_at.add DifferentiableWithinAt.add
@[simp]
theorem DifferentiableAt.add (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
DifferentiableAt π (fun y => f y + g y) x :=
- (hf.HasFderivAt.add hg.HasFderivAt).DifferentiableAt
+ (hf.HasFDerivAt.add hg.HasFDerivAt).DifferentiableAt
#align differentiable_at.add DifferentiableAt.add
theorem DifferentiableOn.add (hf : DifferentiableOn π f s) (hg : DifferentiableOn π g s) :
@@ -168,37 +168,37 @@ theorem Differentiable.add (hf : Differentiable π f) (hg : Differentiable
theorem fderivWithin_add (hxs : UniqueDiffWithinAt π s x) (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) :
fderivWithin π (fun y => f y + g y) s x = fderivWithin π f s x + fderivWithin π g s x :=
- (hf.HasFderivWithinAt.add hg.HasFderivWithinAt).fderivWithin hxs
+ (hf.HasFDerivWithinAt.add hg.HasFDerivWithinAt).fderivWithin hxs
#align fderiv_within_add fderivWithin_add
theorem fderiv_add (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
fderiv π (fun y => f y + g y) x = fderiv π f x + fderiv π g x :=
- (hf.HasFderivAt.add hg.HasFderivAt).fderiv
+ (hf.HasFDerivAt.add hg.HasFDerivAt).fderiv
#align fderiv_add fderiv_add
-theorem HasStrictFderivAt.add_const (hf : HasStrictFderivAt f f' x) (c : F) :
- HasStrictFderivAt (fun y => f y + c) f' x :=
- add_zero f' βΈ hf.add (hasStrictFderivAt_const _ _)
-#align has_strict_fderiv_at.add_const HasStrictFderivAt.add_const
+theorem HasStrictFDerivAt.add_const (hf : HasStrictFDerivAt f f' x) (c : F) :
+ HasStrictFDerivAt (fun y => f y + c) f' x :=
+ add_zero f' βΈ hf.add (hasStrictFDerivAt_const _ _)
+#align has_strict_fderiv_at.add_const HasStrictFDerivAt.add_const
-theorem HasFderivAtFilter.add_const (hf : HasFderivAtFilter f f' x L) (c : F) :
- HasFderivAtFilter (fun y => f y + c) f' x L :=
- add_zero f' βΈ hf.add (hasFderivAtFilter_const _ _ _)
-#align has_fderiv_at_filter.add_const HasFderivAtFilter.add_const
+theorem HasFDerivAtFilter.add_const (hf : HasFDerivAtFilter f f' x L) (c : F) :
+ HasFDerivAtFilter (fun y => f y + c) f' x L :=
+ add_zero f' βΈ hf.add (hasFDerivAtFilter_const _ _ _)
+#align has_fderiv_at_filter.add_const HasFDerivAtFilter.add_const
-theorem HasFderivWithinAt.add_const (hf : HasFderivWithinAt f f' s x) (c : F) :
- HasFderivWithinAt (fun y => f y + c) f' s x :=
+theorem HasFDerivWithinAt.add_const (hf : HasFDerivWithinAt f f' s x) (c : F) :
+ HasFDerivWithinAt (fun y => f y + c) f' s x :=
hf.AddConst c
-#align has_fderiv_within_at.add_const HasFderivWithinAt.add_const
+#align has_fderiv_within_at.add_const HasFDerivWithinAt.add_const
-theorem HasFderivAt.add_const (hf : HasFderivAt f f' x) (c : F) :
- HasFderivAt (fun x => f x + c) f' x :=
+theorem HasFDerivAt.add_const (hf : HasFDerivAt f f' x) (c : F) :
+ HasFDerivAt (fun x => f x + c) f' x :=
hf.AddConst c
-#align has_fderiv_at.add_const HasFderivAt.add_const
+#align has_fderiv_at.add_const HasFDerivAt.add_const
theorem DifferentiableWithinAt.add_const (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => f y + c) s x :=
- (hf.HasFderivWithinAt.AddConst c).DifferentiableWithinAt
+ (hf.HasFDerivWithinAt.AddConst c).DifferentiableWithinAt
#align differentiable_within_at.add_const DifferentiableWithinAt.add_const
@[simp]
@@ -209,7 +209,7 @@ theorem differentiableWithinAt_add_const_iff (c : F) :
theorem DifferentiableAt.add_const (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => f y + c) x :=
- (hf.HasFderivAt.AddConst c).DifferentiableAt
+ (hf.HasFDerivAt.AddConst c).DifferentiableAt
#align differentiable_at.add_const DifferentiableAt.add_const
@[simp]
@@ -240,7 +240,7 @@ theorem differentiable_add_const_iff (c : F) :
theorem fderivWithin_add_const (hxs : UniqueDiffWithinAt π s x) (c : F) :
fderivWithin π (fun y => f y + c) s x = fderivWithin π f s x :=
- if hf : DifferentiableWithinAt π f s x then (hf.HasFderivWithinAt.AddConst c).fderivWithin hxs
+ if hf : DifferentiableWithinAt π f s x then (hf.HasFDerivWithinAt.AddConst c).fderivWithin hxs
else
by
rw [fderivWithin_zero_of_not_differentiableWithinAt hf,
@@ -252,29 +252,29 @@ theorem fderiv_add_const (c : F) : fderiv π (fun y => f y + c) x = fderiv
simp only [β fderivWithin_univ, fderivWithin_add_const uniqueDiffWithinAt_univ]
#align fderiv_add_const fderiv_add_const
-theorem HasStrictFderivAt.const_add (hf : HasStrictFderivAt f f' x) (c : F) :
- HasStrictFderivAt (fun y => c + f y) f' x :=
- zero_add f' βΈ (hasStrictFderivAt_const _ _).add hf
-#align has_strict_fderiv_at.const_add HasStrictFderivAt.const_add
+theorem HasStrictFDerivAt.const_add (hf : HasStrictFDerivAt f f' x) (c : F) :
+ HasStrictFDerivAt (fun y => c + f y) f' x :=
+ zero_add f' βΈ (hasStrictFDerivAt_const _ _).add hf
+#align has_strict_fderiv_at.const_add HasStrictFDerivAt.const_add
-theorem HasFderivAtFilter.const_add (hf : HasFderivAtFilter f f' x L) (c : F) :
- HasFderivAtFilter (fun y => c + f y) f' x L :=
- zero_add f' βΈ (hasFderivAtFilter_const _ _ _).add hf
-#align has_fderiv_at_filter.const_add HasFderivAtFilter.const_add
+theorem HasFDerivAtFilter.const_add (hf : HasFDerivAtFilter f f' x L) (c : F) :
+ HasFDerivAtFilter (fun y => c + f y) f' x L :=
+ zero_add f' βΈ (hasFDerivAtFilter_const _ _ _).add hf
+#align has_fderiv_at_filter.const_add HasFDerivAtFilter.const_add
-theorem HasFderivWithinAt.const_add (hf : HasFderivWithinAt f f' s x) (c : F) :
- HasFderivWithinAt (fun y => c + f y) f' s x :=
+theorem HasFDerivWithinAt.const_add (hf : HasFDerivWithinAt f f' s x) (c : F) :
+ HasFDerivWithinAt (fun y => c + f y) f' s x :=
hf.const_add c
-#align has_fderiv_within_at.const_add HasFderivWithinAt.const_add
+#align has_fderiv_within_at.const_add HasFDerivWithinAt.const_add
-theorem HasFderivAt.const_add (hf : HasFderivAt f f' x) (c : F) :
- HasFderivAt (fun x => c + f x) f' x :=
+theorem HasFDerivAt.const_add (hf : HasFDerivAt f f' x) (c : F) :
+ HasFDerivAt (fun x => c + f x) f' x :=
hf.const_add c
-#align has_fderiv_at.const_add HasFderivAt.const_add
+#align has_fderiv_at.const_add HasFDerivAt.const_add
theorem DifferentiableWithinAt.const_add (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => c + f y) s x :=
- (hf.HasFderivWithinAt.const_add c).DifferentiableWithinAt
+ (hf.HasFDerivWithinAt.const_add c).DifferentiableWithinAt
#align differentiable_within_at.const_add DifferentiableWithinAt.const_add
@[simp]
@@ -285,7 +285,7 @@ theorem differentiableWithinAt_const_add_iff (c : F) :
theorem DifferentiableAt.const_add (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => c + f y) x :=
- (hf.HasFderivAt.const_add c).DifferentiableAt
+ (hf.HasFDerivAt.const_add c).DifferentiableAt
#align differentiable_at.const_add DifferentiableAt.const_add
@[simp]
@@ -334,42 +334,42 @@ open BigOperators
variable {ΞΉ : Type _} {u : Finset ΞΉ} {A : ΞΉ β E β F} {A' : ΞΉ β E βL[π] F}
-theorem HasStrictFderivAt.sum (h : β i β u, HasStrictFderivAt (A i) (A' i) x) :
- HasStrictFderivAt (fun y => β i in u, A i y) (β i in u, A' i) x :=
+theorem HasStrictFDerivAt.sum (h : β i β u, HasStrictFDerivAt (A i) (A' i) x) :
+ HasStrictFDerivAt (fun y => β i in u, A i y) (β i in u, A' i) x :=
by
- dsimp [HasStrictFderivAt] at *
+ dsimp [HasStrictFDerivAt] at *
convert is_o.sum h
simp [Finset.sum_sub_distrib, ContinuousLinearMap.sum_apply]
-#align has_strict_fderiv_at.sum HasStrictFderivAt.sum
+#align has_strict_fderiv_at.sum HasStrictFDerivAt.sum
-theorem HasFderivAtFilter.sum (h : β i β u, HasFderivAtFilter (A i) (A' i) x L) :
- HasFderivAtFilter (fun y => β i in u, A i y) (β i in u, A' i) x L :=
+theorem HasFDerivAtFilter.sum (h : β i β u, HasFDerivAtFilter (A i) (A' i) x L) :
+ HasFDerivAtFilter (fun y => β i in u, A i y) (β i in u, A' i) x L :=
by
- dsimp [HasFderivAtFilter] at *
+ dsimp [HasFDerivAtFilter] at *
convert is_o.sum h
simp [ContinuousLinearMap.sum_apply]
-#align has_fderiv_at_filter.sum HasFderivAtFilter.sum
+#align has_fderiv_at_filter.sum HasFDerivAtFilter.sum
-theorem HasFderivWithinAt.sum (h : β i β u, HasFderivWithinAt (A i) (A' i) s x) :
- HasFderivWithinAt (fun y => β i in u, A i y) (β i in u, A' i) s x :=
- HasFderivAtFilter.sum h
-#align has_fderiv_within_at.sum HasFderivWithinAt.sum
+theorem HasFDerivWithinAt.sum (h : β i β u, HasFDerivWithinAt (A i) (A' i) s x) :
+ HasFDerivWithinAt (fun y => β i in u, A i y) (β i in u, A' i) s x :=
+ HasFDerivAtFilter.sum h
+#align has_fderiv_within_at.sum HasFDerivWithinAt.sum
-theorem HasFderivAt.sum (h : β i β u, HasFderivAt (A i) (A' i) x) :
- HasFderivAt (fun y => β i in u, A i y) (β i in u, A' i) x :=
- HasFderivAtFilter.sum h
-#align has_fderiv_at.sum HasFderivAt.sum
+theorem HasFDerivAt.sum (h : β i β u, HasFDerivAt (A i) (A' i) x) :
+ HasFDerivAt (fun y => β i in u, A i y) (β i in u, A' i) x :=
+ HasFDerivAtFilter.sum h
+#align has_fderiv_at.sum HasFDerivAt.sum
theorem DifferentiableWithinAt.sum (h : β i β u, DifferentiableWithinAt π (A i) s x) :
DifferentiableWithinAt π (fun y => β i in u, A i y) s x :=
- HasFderivWithinAt.differentiableWithinAt <|
- HasFderivWithinAt.sum fun i hi => (h i hi).HasFderivWithinAt
+ HasFDerivWithinAt.differentiableWithinAt <|
+ HasFDerivWithinAt.sum fun i hi => (h i hi).HasFDerivWithinAt
#align differentiable_within_at.sum DifferentiableWithinAt.sum
@[simp]
theorem DifferentiableAt.sum (h : β i β u, DifferentiableAt π (A i) x) :
DifferentiableAt π (fun y => β i in u, A i y) x :=
- HasFderivAt.differentiableAt <| HasFderivAt.sum fun i hi => (h i hi).HasFderivAt
+ HasFDerivAt.differentiableAt <| HasFDerivAt.sum fun i hi => (h i hi).HasFDerivAt
#align differentiable_at.sum DifferentiableAt.sum
theorem DifferentiableOn.sum (h : β i β u, DifferentiableOn π (A i) s) :
@@ -385,12 +385,12 @@ theorem Differentiable.sum (h : β i β u, Differentiable π (A i)) :
theorem fderivWithin_sum (hxs : UniqueDiffWithinAt π s x)
(h : β i β u, DifferentiableWithinAt π (A i) s x) :
fderivWithin π (fun y => β i in u, A i y) s x = β i in u, fderivWithin π (A i) s x :=
- (HasFderivWithinAt.sum fun i hi => (h i hi).HasFderivWithinAt).fderivWithin hxs
+ (HasFDerivWithinAt.sum fun i hi => (h i hi).HasFDerivWithinAt).fderivWithin hxs
#align fderiv_within_sum fderivWithin_sum
theorem fderiv_sum (h : β i β u, DifferentiableAt π (A i) x) :
fderiv π (fun y => β i in u, A i y) x = β i in u, fderiv π (A i) x :=
- (HasFderivAt.sum fun i hi => (h i hi).HasFderivAt).fderiv
+ (HasFDerivAt.sum fun i hi => (h i hi).HasFDerivAt).fderiv
#align fderiv_sum fderiv_sum
end Sum
@@ -400,28 +400,28 @@ section Neg
/-! ### Derivative of the negative of a function -/
-theorem HasStrictFderivAt.neg (h : HasStrictFderivAt f f' x) :
- HasStrictFderivAt (fun x => -f x) (-f') x :=
- (-1 : F βL[π] F).HasStrictFderivAt.comp x h
-#align has_strict_fderiv_at.neg HasStrictFderivAt.neg
+theorem HasStrictFDerivAt.neg (h : HasStrictFDerivAt f f' x) :
+ HasStrictFDerivAt (fun x => -f x) (-f') x :=
+ (-1 : F βL[π] F).HasStrictFDerivAt.comp x h
+#align has_strict_fderiv_at.neg HasStrictFDerivAt.neg
-theorem HasFderivAtFilter.neg (h : HasFderivAtFilter f f' x L) :
- HasFderivAtFilter (fun x => -f x) (-f') x L :=
- (-1 : F βL[π] F).HasFderivAtFilter.comp x h tendsto_map
-#align has_fderiv_at_filter.neg HasFderivAtFilter.neg
+theorem HasFDerivAtFilter.neg (h : HasFDerivAtFilter f f' x L) :
+ HasFDerivAtFilter (fun x => -f x) (-f') x L :=
+ (-1 : F βL[π] F).HasFDerivAtFilter.comp x h tendsto_map
+#align has_fderiv_at_filter.neg HasFDerivAtFilter.neg
-theorem HasFderivWithinAt.neg (h : HasFderivWithinAt f f' s x) :
- HasFderivWithinAt (fun x => -f x) (-f') s x :=
+theorem HasFDerivWithinAt.neg (h : HasFDerivWithinAt f f' s x) :
+ HasFDerivWithinAt (fun x => -f x) (-f') s x :=
h.neg
-#align has_fderiv_within_at.neg HasFderivWithinAt.neg
+#align has_fderiv_within_at.neg HasFDerivWithinAt.neg
-theorem HasFderivAt.neg (h : HasFderivAt f f' x) : HasFderivAt (fun x => -f x) (-f') x :=
+theorem HasFDerivAt.neg (h : HasFDerivAt f f' x) : HasFDerivAt (fun x => -f x) (-f') x :=
h.neg
-#align has_fderiv_at.neg HasFderivAt.neg
+#align has_fderiv_at.neg HasFDerivAt.neg
theorem DifferentiableWithinAt.neg (h : DifferentiableWithinAt π f s x) :
DifferentiableWithinAt π (fun y => -f y) s x :=
- h.HasFderivWithinAt.neg.DifferentiableWithinAt
+ h.HasFDerivWithinAt.neg.DifferentiableWithinAt
#align differentiable_within_at.neg DifferentiableWithinAt.neg
@[simp]
@@ -431,7 +431,7 @@ theorem differentiableWithinAt_neg_iff :
#align differentiable_within_at_neg_iff differentiableWithinAt_neg_iff
theorem DifferentiableAt.neg (h : DifferentiableAt π f x) : DifferentiableAt π (fun y => -f y) x :=
- h.HasFderivAt.neg.DifferentiableAt
+ h.HasFDerivAt.neg.DifferentiableAt
#align differentiable_at.neg DifferentiableAt.neg
@[simp]
@@ -459,7 +459,7 @@ theorem differentiable_neg_iff : (Differentiable π fun y => -f y) β Differe
theorem fderivWithin_neg (hxs : UniqueDiffWithinAt π s x) :
fderivWithin π (fun y => -f y) s x = -fderivWithin π f s x :=
- if h : DifferentiableWithinAt π f s x then h.HasFderivWithinAt.neg.fderivWithin hxs
+ if h : DifferentiableWithinAt π f s x then h.HasFDerivWithinAt.neg.fderivWithin hxs
else
by
rw [fderivWithin_zero_of_not_differentiableWithinAt h,
@@ -479,35 +479,35 @@ section Sub
/-! ### Derivative of the difference of two functions -/
-theorem HasStrictFderivAt.sub (hf : HasStrictFderivAt f f' x) (hg : HasStrictFderivAt g g' x) :
- HasStrictFderivAt (fun x => f x - g x) (f' - g') x := by
+theorem HasStrictFDerivAt.sub (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDerivAt g g' x) :
+ HasStrictFDerivAt (fun x => f x - g x) (f' - g') x := by
simpa only [sub_eq_add_neg] using hf.add hg.neg
-#align has_strict_fderiv_at.sub HasStrictFderivAt.sub
+#align has_strict_fderiv_at.sub HasStrictFDerivAt.sub
-theorem HasFderivAtFilter.sub (hf : HasFderivAtFilter f f' x L) (hg : HasFderivAtFilter g g' x L) :
- HasFderivAtFilter (fun x => f x - g x) (f' - g') x L := by
+theorem HasFDerivAtFilter.sub (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivAtFilter g g' x L) :
+ HasFDerivAtFilter (fun x => f x - g x) (f' - g') x L := by
simpa only [sub_eq_add_neg] using hf.add hg.neg
-#align has_fderiv_at_filter.sub HasFderivAtFilter.sub
+#align has_fderiv_at_filter.sub HasFDerivAtFilter.sub
-theorem HasFderivWithinAt.sub (hf : HasFderivWithinAt f f' s x) (hg : HasFderivWithinAt g g' s x) :
- HasFderivWithinAt (fun x => f x - g x) (f' - g') s x :=
+theorem HasFDerivWithinAt.sub (hf : HasFDerivWithinAt f f' s x) (hg : HasFDerivWithinAt g g' s x) :
+ HasFDerivWithinAt (fun x => f x - g x) (f' - g') s x :=
hf.sub hg
-#align has_fderiv_within_at.sub HasFderivWithinAt.sub
+#align has_fderiv_within_at.sub HasFDerivWithinAt.sub
-theorem HasFderivAt.sub (hf : HasFderivAt f f' x) (hg : HasFderivAt g g' x) :
- HasFderivAt (fun x => f x - g x) (f' - g') x :=
+theorem HasFDerivAt.sub (hf : HasFDerivAt f f' x) (hg : HasFDerivAt g g' x) :
+ HasFDerivAt (fun x => f x - g x) (f' - g') x :=
hf.sub hg
-#align has_fderiv_at.sub HasFderivAt.sub
+#align has_fderiv_at.sub HasFDerivAt.sub
theorem DifferentiableWithinAt.sub (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) : DifferentiableWithinAt π (fun y => f y - g y) s x :=
- (hf.HasFderivWithinAt.sub hg.HasFderivWithinAt).DifferentiableWithinAt
+ (hf.HasFDerivWithinAt.sub hg.HasFDerivWithinAt).DifferentiableWithinAt
#align differentiable_within_at.sub DifferentiableWithinAt.sub
@[simp]
theorem DifferentiableAt.sub (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
DifferentiableAt π (fun y => f y - g y) x :=
- (hf.HasFderivAt.sub hg.HasFderivAt).DifferentiableAt
+ (hf.HasFDerivAt.sub hg.HasFDerivAt).DifferentiableAt
#align differentiable_at.sub DifferentiableAt.sub
theorem DifferentiableOn.sub (hf : DifferentiableOn π f s) (hg : DifferentiableOn π g s) :
@@ -522,37 +522,37 @@ theorem Differentiable.sub (hf : Differentiable π f) (hg : Differentiable
theorem fderivWithin_sub (hxs : UniqueDiffWithinAt π s x) (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) :
fderivWithin π (fun y => f y - g y) s x = fderivWithin π f s x - fderivWithin π g s x :=
- (hf.HasFderivWithinAt.sub hg.HasFderivWithinAt).fderivWithin hxs
+ (hf.HasFDerivWithinAt.sub hg.HasFDerivWithinAt).fderivWithin hxs
#align fderiv_within_sub fderivWithin_sub
theorem fderiv_sub (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
fderiv π (fun y => f y - g y) x = fderiv π f x - fderiv π g x :=
- (hf.HasFderivAt.sub hg.HasFderivAt).fderiv
+ (hf.HasFDerivAt.sub hg.HasFDerivAt).fderiv
#align fderiv_sub fderiv_sub
-theorem HasStrictFderivAt.sub_const (hf : HasStrictFderivAt f f' x) (c : F) :
- HasStrictFderivAt (fun x => f x - c) f' x := by
+theorem HasStrictFDerivAt.sub_const (hf : HasStrictFDerivAt f f' x) (c : F) :
+ HasStrictFDerivAt (fun x => f x - c) f' x := by
simpa only [sub_eq_add_neg] using hf.add_const (-c)
-#align has_strict_fderiv_at.sub_const HasStrictFderivAt.sub_const
+#align has_strict_fderiv_at.sub_const HasStrictFDerivAt.sub_const
-theorem HasFderivAtFilter.sub_const (hf : HasFderivAtFilter f f' x L) (c : F) :
- HasFderivAtFilter (fun x => f x - c) f' x L := by
+theorem HasFDerivAtFilter.sub_const (hf : HasFDerivAtFilter f f' x L) (c : F) :
+ HasFDerivAtFilter (fun x => f x - c) f' x L := by
simpa only [sub_eq_add_neg] using hf.add_const (-c)
-#align has_fderiv_at_filter.sub_const HasFderivAtFilter.sub_const
+#align has_fderiv_at_filter.sub_const HasFDerivAtFilter.sub_const
-theorem HasFderivWithinAt.sub_const (hf : HasFderivWithinAt f f' s x) (c : F) :
- HasFderivWithinAt (fun x => f x - c) f' s x :=
+theorem HasFDerivWithinAt.sub_const (hf : HasFDerivWithinAt f f' s x) (c : F) :
+ HasFDerivWithinAt (fun x => f x - c) f' s x :=
hf.sub_const c
-#align has_fderiv_within_at.sub_const HasFderivWithinAt.sub_const
+#align has_fderiv_within_at.sub_const HasFDerivWithinAt.sub_const
-theorem HasFderivAt.sub_const (hf : HasFderivAt f f' x) (c : F) :
- HasFderivAt (fun x => f x - c) f' x :=
+theorem HasFDerivAt.sub_const (hf : HasFDerivAt f f' x) (c : F) :
+ HasFDerivAt (fun x => f x - c) f' x :=
hf.sub_const c
-#align has_fderiv_at.sub_const HasFderivAt.sub_const
+#align has_fderiv_at.sub_const HasFDerivAt.sub_const
theorem DifferentiableWithinAt.sub_const (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => f y - c) s x :=
- (hf.HasFderivWithinAt.sub_const c).DifferentiableWithinAt
+ (hf.HasFDerivWithinAt.sub_const c).DifferentiableWithinAt
#align differentiable_within_at.sub_const DifferentiableWithinAt.sub_const
@[simp]
@@ -563,7 +563,7 @@ theorem differentiableWithinAt_sub_const_iff (c : F) :
theorem DifferentiableAt.sub_const (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => f y - c) x :=
- (hf.HasFderivAt.sub_const c).DifferentiableAt
+ (hf.HasFDerivAt.sub_const c).DifferentiableAt
#align differentiable_at.sub_const DifferentiableAt.sub_const
@[simp]
@@ -601,29 +601,29 @@ theorem fderiv_sub_const (c : F) : fderiv π (fun y => f y - c) x = fderiv
simp only [sub_eq_add_neg, fderiv_add_const]
#align fderiv_sub_const fderiv_sub_const
-theorem HasStrictFderivAt.const_sub (hf : HasStrictFderivAt f f' x) (c : F) :
- HasStrictFderivAt (fun x => c - f x) (-f') x := by
+theorem HasStrictFDerivAt.const_sub (hf : HasStrictFDerivAt f f' x) (c : F) :
+ HasStrictFDerivAt (fun x => c - f x) (-f') x := by
simpa only [sub_eq_add_neg] using hf.neg.const_add c
-#align has_strict_fderiv_at.const_sub HasStrictFderivAt.const_sub
+#align has_strict_fderiv_at.const_sub HasStrictFDerivAt.const_sub
-theorem HasFderivAtFilter.const_sub (hf : HasFderivAtFilter f f' x L) (c : F) :
- HasFderivAtFilter (fun x => c - f x) (-f') x L := by
+theorem HasFDerivAtFilter.const_sub (hf : HasFDerivAtFilter f f' x L) (c : F) :
+ HasFDerivAtFilter (fun x => c - f x) (-f') x L := by
simpa only [sub_eq_add_neg] using hf.neg.const_add c
-#align has_fderiv_at_filter.const_sub HasFderivAtFilter.const_sub
+#align has_fderiv_at_filter.const_sub HasFDerivAtFilter.const_sub
-theorem HasFderivWithinAt.const_sub (hf : HasFderivWithinAt f f' s x) (c : F) :
- HasFderivWithinAt (fun x => c - f x) (-f') s x :=
+theorem HasFDerivWithinAt.const_sub (hf : HasFDerivWithinAt f f' s x) (c : F) :
+ HasFDerivWithinAt (fun x => c - f x) (-f') s x :=
hf.const_sub c
-#align has_fderiv_within_at.const_sub HasFderivWithinAt.const_sub
+#align has_fderiv_within_at.const_sub HasFDerivWithinAt.const_sub
-theorem HasFderivAt.const_sub (hf : HasFderivAt f f' x) (c : F) :
- HasFderivAt (fun x => c - f x) (-f') x :=
+theorem HasFDerivAt.const_sub (hf : HasFDerivAt f f' x) (c : F) :
+ HasFDerivAt (fun x => c - f x) (-f') x :=
hf.const_sub c
-#align has_fderiv_at.const_sub HasFderivAt.const_sub
+#align has_fderiv_at.const_sub HasFDerivAt.const_sub
theorem DifferentiableWithinAt.const_sub (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => c - f y) s x :=
- (hf.HasFderivWithinAt.const_sub c).DifferentiableWithinAt
+ (hf.HasFDerivWithinAt.const_sub c).DifferentiableWithinAt
#align differentiable_within_at.const_sub DifferentiableWithinAt.const_sub
@[simp]
@@ -634,7 +634,7 @@ theorem differentiableWithinAt_const_sub_iff (c : F) :
theorem DifferentiableAt.const_sub (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => c - f y) x :=
- (hf.HasFderivAt.const_sub c).DifferentiableAt
+ (hf.HasFDerivAt.const_sub c).DifferentiableAt
#align differentiable_at.const_sub DifferentiableAt.const_sub
@[simp]
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)
@@ -33,25 +33,15 @@ noncomputable section
section
variable {π : Type*} [NontriviallyNormedField π]
-
variable {E : Type*} [NormedAddCommGroup E] [NormedSpace π E]
-
variable {F : Type*} [NormedAddCommGroup F] [NormedSpace π F]
-
variable {G : Type*} [NormedAddCommGroup G] [NormedSpace π G]
-
variable {G' : Type*} [NormedAddCommGroup G'] [NormedSpace π G']
-
variable {f fβ fβ g : E β F}
-
variable {f' fβ' fβ' g' : E βL[π] F}
-
variable (e : E βL[π] F)
-
variable {x : E}
-
variable {s t : Set E}
-
variable {L Lβ Lβ : Filter E}
section ConstSMul
Basic setup for fun_prop
for Differentiable(At/On/Within) and HasFDeriv(At/Within/Strict).
Mainly consists of marking theorems with fun_prop
attribute but I had to formulate appropriate _pi
and _apply
theorems. Proofs of _apply
theorems can probably be golfed into neater form.
@@ -60,7 +60,7 @@ variable {R : Type*} [Semiring R] [Module R F] [SMulCommClass π R F] [Continu
/-! ### Derivative of a function multiplied by a constant -/
-
+@[fun_prop]
theorem HasStrictFDerivAt.const_smul (h : HasStrictFDerivAt f f' x) (c : R) :
HasStrictFDerivAt (fun x => c β’ f x) (c β’ f') x :=
(c β’ (1 : F βL[π] F)).hasStrictFDerivAt.comp x h
@@ -71,30 +71,36 @@ theorem HasFDerivAtFilter.const_smul (h : HasFDerivAtFilter f f' x L) (c : R) :
(c β’ (1 : F βL[π] F)).hasFDerivAtFilter.comp x h tendsto_map
#align has_fderiv_at_filter.const_smul HasFDerivAtFilter.const_smul
+@[fun_prop]
nonrec theorem HasFDerivWithinAt.const_smul (h : HasFDerivWithinAt f f' s x) (c : R) :
HasFDerivWithinAt (fun x => c β’ f x) (c β’ f') s x :=
h.const_smul c
#align has_fderiv_within_at.const_smul HasFDerivWithinAt.const_smul
+@[fun_prop]
nonrec theorem HasFDerivAt.const_smul (h : HasFDerivAt f f' x) (c : R) :
HasFDerivAt (fun x => c β’ f x) (c β’ f') x :=
h.const_smul c
#align has_fderiv_at.const_smul HasFDerivAt.const_smul
+@[fun_prop]
theorem DifferentiableWithinAt.const_smul (h : DifferentiableWithinAt π f s x) (c : R) :
DifferentiableWithinAt π (fun y => c β’ f y) s x :=
(h.hasFDerivWithinAt.const_smul c).differentiableWithinAt
#align differentiable_within_at.const_smul DifferentiableWithinAt.const_smul
+@[fun_prop]
theorem DifferentiableAt.const_smul (h : DifferentiableAt π f x) (c : R) :
DifferentiableAt π (fun y => c β’ f y) x :=
(h.hasFDerivAt.const_smul c).differentiableAt
#align differentiable_at.const_smul DifferentiableAt.const_smul
+@[fun_prop]
theorem DifferentiableOn.const_smul (h : DifferentiableOn π f s) (c : R) :
DifferentiableOn π (fun y => c β’ f y) s := fun x hx => (h x hx).const_smul c
#align differentiable_on.const_smul DifferentiableOn.const_smul
+@[fun_prop]
theorem Differentiable.const_smul (h : Differentiable π f) (c : R) :
Differentiable π fun y => c β’ f y := fun x => (h x).const_smul c
#align differentiable.const_smul Differentiable.const_smul
@@ -117,6 +123,7 @@ section Add
/-! ### Derivative of the sum of two functions -/
+@[fun_prop]
nonrec theorem HasStrictFDerivAt.add (hf : HasStrictFDerivAt f f' x)
(hg : HasStrictFDerivAt g g' x) : HasStrictFDerivAt (fun y => f y + g y) (f' + g') x :=
(hf.add hg).congr_left fun y => by
@@ -131,32 +138,36 @@ theorem HasFDerivAtFilter.add (hf : HasFDerivAtFilter f f' x L)
abel
#align has_fderiv_at_filter.add HasFDerivAtFilter.add
+@[fun_prop]
nonrec theorem HasFDerivWithinAt.add (hf : HasFDerivWithinAt f f' s x)
(hg : HasFDerivWithinAt g g' s x) : HasFDerivWithinAt (fun y => f y + g y) (f' + g') s x :=
hf.add hg
#align has_fderiv_within_at.add HasFDerivWithinAt.add
+@[fun_prop]
nonrec theorem HasFDerivAt.add (hf : HasFDerivAt f f' x) (hg : HasFDerivAt g g' x) :
HasFDerivAt (fun x => f x + g x) (f' + g') x :=
hf.add hg
#align has_fderiv_at.add HasFDerivAt.add
+@[fun_prop]
theorem DifferentiableWithinAt.add (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) : DifferentiableWithinAt π (fun y => f y + g y) s x :=
(hf.hasFDerivWithinAt.add hg.hasFDerivWithinAt).differentiableWithinAt
#align differentiable_within_at.add DifferentiableWithinAt.add
-@[simp]
+@[simp, fun_prop]
theorem DifferentiableAt.add (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
DifferentiableAt π (fun y => f y + g y) x :=
(hf.hasFDerivAt.add hg.hasFDerivAt).differentiableAt
#align differentiable_at.add DifferentiableAt.add
+@[fun_prop]
theorem DifferentiableOn.add (hf : DifferentiableOn π f s) (hg : DifferentiableOn π g s) :
DifferentiableOn π (fun y => f y + g y) s := fun x hx => (hf x hx).add (hg x hx)
#align differentiable_on.add DifferentiableOn.add
-@[simp]
+@[simp, fun_prop]
theorem Differentiable.add (hf : Differentiable π f) (hg : Differentiable π g) :
Differentiable π fun y => f y + g y := fun x => (hf x).add (hg x)
#align differentiable.add Differentiable.add
@@ -172,6 +183,7 @@ theorem fderiv_add (hf : DifferentiableAt π f x) (hg : DifferentiableAt π
(hf.hasFDerivAt.add hg.hasFDerivAt).fderiv
#align fderiv_add fderiv_add
+@[fun_prop]
theorem HasStrictFDerivAt.add_const (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun y => f y + c) f' x :=
add_zero f' βΈ hf.add (hasStrictFDerivAt_const _ _)
@@ -182,16 +194,19 @@ theorem HasFDerivAtFilter.add_const (hf : HasFDerivAtFilter f f' x L) (c : F) :
add_zero f' βΈ hf.add (hasFDerivAtFilter_const _ _ _)
#align has_fderiv_at_filter.add_const HasFDerivAtFilter.add_const
+@[fun_prop]
nonrec theorem HasFDerivWithinAt.add_const (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun y => f y + c) f' s x :=
hf.add_const c
#align has_fderiv_within_at.add_const HasFDerivWithinAt.add_const
+@[fun_prop]
nonrec theorem HasFDerivAt.add_const (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => f x + c) f' x :=
hf.add_const c
#align has_fderiv_at.add_const HasFDerivAt.add_const
+@[fun_prop]
theorem DifferentiableWithinAt.add_const (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => f y + c) s x :=
(hf.hasFDerivWithinAt.add_const c).differentiableWithinAt
@@ -203,6 +218,7 @@ theorem differentiableWithinAt_add_const_iff (c : F) :
β¨fun h => by simpa using h.add_const (-c), fun h => h.add_const cβ©
#align differentiable_within_at_add_const_iff differentiableWithinAt_add_const_iff
+@[fun_prop]
theorem DifferentiableAt.add_const (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => f y + c) x :=
(hf.hasFDerivAt.add_const c).differentiableAt
@@ -214,6 +230,7 @@ theorem differentiableAt_add_const_iff (c : F) :
β¨fun h => by simpa using h.add_const (-c), fun h => h.add_const cβ©
#align differentiable_at_add_const_iff differentiableAt_add_const_iff
+@[fun_prop]
theorem DifferentiableOn.add_const (hf : DifferentiableOn π f s) (c : F) :
DifferentiableOn π (fun y => f y + c) s := fun x hx => (hf x hx).add_const c
#align differentiable_on.add_const DifferentiableOn.add_const
@@ -224,6 +241,7 @@ theorem differentiableOn_add_const_iff (c : F) :
β¨fun h => by simpa using h.add_const (-c), fun h => h.add_const cβ©
#align differentiable_on_add_const_iff differentiableOn_add_const_iff
+@[fun_prop]
theorem Differentiable.add_const (hf : Differentiable π f) (c : F) :
Differentiable π fun y => f y + c := fun x => (hf x).add_const c
#align differentiable.add_const Differentiable.add_const
@@ -247,6 +265,7 @@ theorem fderiv_add_const (c : F) : fderiv π (fun y => f y + c) x = fderiv
simp only [β fderivWithin_univ, fderivWithin_add_const uniqueDiffWithinAt_univ]
#align fderiv_add_const fderiv_add_const
+@[fun_prop]
theorem HasStrictFDerivAt.const_add (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun y => c + f y) f' x :=
zero_add f' βΈ (hasStrictFDerivAt_const _ _).add hf
@@ -257,16 +276,19 @@ theorem HasFDerivAtFilter.const_add (hf : HasFDerivAtFilter f f' x L) (c : F) :
zero_add f' βΈ (hasFDerivAtFilter_const _ _ _).add hf
#align has_fderiv_at_filter.const_add HasFDerivAtFilter.const_add
+@[fun_prop]
nonrec theorem HasFDerivWithinAt.const_add (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun y => c + f y) f' s x :=
hf.const_add c
#align has_fderiv_within_at.const_add HasFDerivWithinAt.const_add
+@[fun_prop]
nonrec theorem HasFDerivAt.const_add (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => c + f x) f' x :=
hf.const_add c
#align has_fderiv_at.const_add HasFDerivAt.const_add
+@[fun_prop]
theorem DifferentiableWithinAt.const_add (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => c + f y) s x :=
(hf.hasFDerivWithinAt.const_add c).differentiableWithinAt
@@ -278,6 +300,7 @@ theorem differentiableWithinAt_const_add_iff (c : F) :
β¨fun h => by simpa using h.const_add (-c), fun h => h.const_add cβ©
#align differentiable_within_at_const_add_iff differentiableWithinAt_const_add_iff
+@[fun_prop]
theorem DifferentiableAt.const_add (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => c + f y) x :=
(hf.hasFDerivAt.const_add c).differentiableAt
@@ -289,6 +312,7 @@ theorem differentiableAt_const_add_iff (c : F) :
β¨fun h => by simpa using h.const_add (-c), fun h => h.const_add cβ©
#align differentiable_at_const_add_iff differentiableAt_const_add_iff
+@[fun_prop]
theorem DifferentiableOn.const_add (hf : DifferentiableOn π f s) (c : F) :
DifferentiableOn π (fun y => c + f y) s := fun x hx => (hf x hx).const_add c
#align differentiable_on.const_add DifferentiableOn.const_add
@@ -299,6 +323,7 @@ theorem differentiableOn_const_add_iff (c : F) :
β¨fun h => by simpa using h.const_add (-c), fun h => h.const_add cβ©
#align differentiable_on_const_add_iff differentiableOn_const_add_iff
+@[fun_prop]
theorem Differentiable.const_add (hf : Differentiable π f) (c : F) :
Differentiable π fun y => c + f y := fun x => (hf x).const_add c
#align differentiable.const_add Differentiable.const_add
@@ -329,6 +354,7 @@ open BigOperators
variable {ΞΉ : Type*} {u : Finset ΞΉ} {A : ΞΉ β E β F} {A' : ΞΉ β E βL[π] F}
+@[fun_prop]
theorem HasStrictFDerivAt.sum (h : β i β u, HasStrictFDerivAt (A i) (A' i) x) :
HasStrictFDerivAt (fun y => β i in u, A i y) (β i in u, A' i) x := by
dsimp [HasStrictFDerivAt] at *
@@ -343,34 +369,38 @@ theorem HasFDerivAtFilter.sum (h : β i β u, HasFDerivAtFilter (A i) (A' i) x
simp [ContinuousLinearMap.sum_apply]
#align has_fderiv_at_filter.sum HasFDerivAtFilter.sum
+@[fun_prop]
theorem HasFDerivWithinAt.sum (h : β i β u, HasFDerivWithinAt (A i) (A' i) s x) :
HasFDerivWithinAt (fun y => β i in u, A i y) (β i in u, A' i) s x :=
HasFDerivAtFilter.sum h
#align has_fderiv_within_at.sum HasFDerivWithinAt.sum
+@[fun_prop]
theorem HasFDerivAt.sum (h : β i β u, HasFDerivAt (A i) (A' i) x) :
HasFDerivAt (fun y => β i in u, A i y) (β i in u, A' i) x :=
HasFDerivAtFilter.sum h
#align has_fderiv_at.sum HasFDerivAt.sum
+@[fun_prop]
theorem DifferentiableWithinAt.sum (h : β i β u, DifferentiableWithinAt π (A i) s x) :
DifferentiableWithinAt π (fun y => β i in u, A i y) s x :=
HasFDerivWithinAt.differentiableWithinAt <|
HasFDerivWithinAt.sum fun i hi => (h i hi).hasFDerivWithinAt
#align differentiable_within_at.sum DifferentiableWithinAt.sum
-@[simp]
+@[simp, fun_prop]
theorem DifferentiableAt.sum (h : β i β u, DifferentiableAt π (A i) x) :
DifferentiableAt π (fun y => β i in u, A i y) x :=
HasFDerivAt.differentiableAt <| HasFDerivAt.sum fun i hi => (h i hi).hasFDerivAt
#align differentiable_at.sum DifferentiableAt.sum
+@[fun_prop]
theorem DifferentiableOn.sum (h : β i β u, DifferentiableOn π (A i) s) :
DifferentiableOn π (fun y => β i in u, A i y) s := fun x hx =>
DifferentiableWithinAt.sum fun i hi => h i hi x hx
#align differentiable_on.sum DifferentiableOn.sum
-@[simp]
+@[simp, fun_prop]
theorem Differentiable.sum (h : β i β u, Differentiable π (A i)) :
Differentiable π fun y => β i in u, A i y := fun x => DifferentiableAt.sum fun i hi => h i hi x
#align differentiable.sum Differentiable.sum
@@ -393,6 +423,7 @@ section Neg
/-! ### Derivative of the negative of a function -/
+@[fun_prop]
theorem HasStrictFDerivAt.neg (h : HasStrictFDerivAt f f' x) :
HasStrictFDerivAt (fun x => -f x) (-f') x :=
(-1 : F βL[π] F).hasStrictFDerivAt.comp x h
@@ -403,15 +434,18 @@ theorem HasFDerivAtFilter.neg (h : HasFDerivAtFilter f f' x L) :
(-1 : F βL[π] F).hasFDerivAtFilter.comp x h tendsto_map
#align has_fderiv_at_filter.neg HasFDerivAtFilter.neg
+@[fun_prop]
nonrec theorem HasFDerivWithinAt.neg (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt (fun x => -f x) (-f') s x :=
h.neg
#align has_fderiv_within_at.neg HasFDerivWithinAt.neg
+@[fun_prop]
nonrec theorem HasFDerivAt.neg (h : HasFDerivAt f f' x) : HasFDerivAt (fun x => -f x) (-f') x :=
h.neg
#align has_fderiv_at.neg HasFDerivAt.neg
+@[fun_prop]
theorem DifferentiableWithinAt.neg (h : DifferentiableWithinAt π f s x) :
DifferentiableWithinAt π (fun y => -f y) s x :=
h.hasFDerivWithinAt.neg.differentiableWithinAt
@@ -423,6 +457,7 @@ theorem differentiableWithinAt_neg_iff :
β¨fun h => by simpa only [neg_neg] using h.neg, fun h => h.negβ©
#align differentiable_within_at_neg_iff differentiableWithinAt_neg_iff
+@[fun_prop]
theorem DifferentiableAt.neg (h : DifferentiableAt π f x) : DifferentiableAt π (fun y => -f y) x :=
h.hasFDerivAt.neg.differentiableAt
#align differentiable_at.neg DifferentiableAt.neg
@@ -432,6 +467,7 @@ theorem differentiableAt_neg_iff : DifferentiableAt π (fun y => -f y) x β D
β¨fun h => by simpa only [neg_neg] using h.neg, fun h => h.negβ©
#align differentiable_at_neg_iff differentiableAt_neg_iff
+@[fun_prop]
theorem DifferentiableOn.neg (h : DifferentiableOn π f s) : DifferentiableOn π (fun y => -f y) s :=
fun x hx => (h x hx).neg
#align differentiable_on.neg DifferentiableOn.neg
@@ -441,6 +477,7 @@ theorem differentiableOn_neg_iff : DifferentiableOn π (fun y => -f y) s β D
β¨fun h => by simpa only [neg_neg] using h.neg, fun h => h.negβ©
#align differentiable_on_neg_iff differentiableOn_neg_iff
+@[fun_prop]
theorem Differentiable.neg (h : Differentiable π f) : Differentiable π fun y => -f y := fun x =>
(h x).neg
#align differentiable.neg Differentiable.neg
@@ -471,6 +508,7 @@ section Sub
/-! ### Derivative of the difference of two functions -/
+@[fun_prop]
theorem HasStrictFDerivAt.sub (hf : HasStrictFDerivAt f f' x) (hg : HasStrictFDerivAt g g' x) :
HasStrictFDerivAt (fun x => f x - g x) (f' - g') x := by
simpa only [sub_eq_add_neg] using hf.add hg.neg
@@ -481,32 +519,36 @@ theorem HasFDerivAtFilter.sub (hf : HasFDerivAtFilter f f' x L) (hg : HasFDerivA
simpa only [sub_eq_add_neg] using hf.add hg.neg
#align has_fderiv_at_filter.sub HasFDerivAtFilter.sub
+@[fun_prop]
nonrec theorem HasFDerivWithinAt.sub (hf : HasFDerivWithinAt f f' s x)
(hg : HasFDerivWithinAt g g' s x) : HasFDerivWithinAt (fun x => f x - g x) (f' - g') s x :=
hf.sub hg
#align has_fderiv_within_at.sub HasFDerivWithinAt.sub
+@[fun_prop]
nonrec theorem HasFDerivAt.sub (hf : HasFDerivAt f f' x) (hg : HasFDerivAt g g' x) :
HasFDerivAt (fun x => f x - g x) (f' - g') x :=
hf.sub hg
#align has_fderiv_at.sub HasFDerivAt.sub
+@[fun_prop]
theorem DifferentiableWithinAt.sub (hf : DifferentiableWithinAt π f s x)
(hg : DifferentiableWithinAt π g s x) : DifferentiableWithinAt π (fun y => f y - g y) s x :=
(hf.hasFDerivWithinAt.sub hg.hasFDerivWithinAt).differentiableWithinAt
#align differentiable_within_at.sub DifferentiableWithinAt.sub
-@[simp]
+@[simp, fun_prop]
theorem DifferentiableAt.sub (hf : DifferentiableAt π f x) (hg : DifferentiableAt π g x) :
DifferentiableAt π (fun y => f y - g y) x :=
(hf.hasFDerivAt.sub hg.hasFDerivAt).differentiableAt
#align differentiable_at.sub DifferentiableAt.sub
+@[fun_prop]
theorem DifferentiableOn.sub (hf : DifferentiableOn π f s) (hg : DifferentiableOn π g s) :
DifferentiableOn π (fun y => f y - g y) s := fun x hx => (hf x hx).sub (hg x hx)
#align differentiable_on.sub DifferentiableOn.sub
-@[simp]
+@[simp, fun_prop]
theorem Differentiable.sub (hf : Differentiable π f) (hg : Differentiable π g) :
Differentiable π fun y => f y - g y := fun x => (hf x).sub (hg x)
#align differentiable.sub Differentiable.sub
@@ -522,6 +564,7 @@ theorem fderiv_sub (hf : DifferentiableAt π f x) (hg : DifferentiableAt π
(hf.hasFDerivAt.sub hg.hasFDerivAt).fderiv
#align fderiv_sub fderiv_sub
+@[fun_prop]
theorem HasStrictFDerivAt.sub_const (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun x => f x - c) f' x := by
simpa only [sub_eq_add_neg] using hf.add_const (-c)
@@ -532,22 +575,27 @@ theorem HasFDerivAtFilter.sub_const (hf : HasFDerivAtFilter f f' x L) (c : F) :
simpa only [sub_eq_add_neg] using hf.add_const (-c)
#align has_fderiv_at_filter.sub_const HasFDerivAtFilter.sub_const
+@[fun_prop]
nonrec theorem HasFDerivWithinAt.sub_const (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun x => f x - c) f' s x :=
hf.sub_const c
#align has_fderiv_within_at.sub_const HasFDerivWithinAt.sub_const
+@[fun_prop]
nonrec theorem HasFDerivAt.sub_const (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => f x - c) f' x :=
hf.sub_const c
#align has_fderiv_at.sub_const HasFDerivAt.sub_const
+@[fun_prop]
theorem hasStrictFDerivAt_sub_const {x : F} (c : F) : HasStrictFDerivAt (Β· - c) (id π F) x :=
(hasStrictFDerivAt_id x).sub_const c
+@[fun_prop]
theorem hasFDerivAt_sub_const {x : F} (c : F) : HasFDerivAt (Β· - c) (id π F) x :=
(hasFDerivAt_id x).sub_const c
+@[fun_prop]
theorem DifferentiableWithinAt.sub_const (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => f y - c) s x :=
(hf.hasFDerivWithinAt.sub_const c).differentiableWithinAt
@@ -559,6 +607,7 @@ theorem differentiableWithinAt_sub_const_iff (c : F) :
simp only [sub_eq_add_neg, differentiableWithinAt_add_const_iff]
#align differentiable_within_at_sub_const_iff differentiableWithinAt_sub_const_iff
+@[fun_prop]
theorem DifferentiableAt.sub_const (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => f y - c) x :=
(hf.hasFDerivAt.sub_const c).differentiableAt
@@ -570,6 +619,7 @@ theorem differentiableAt_sub_const_iff (c : F) :
simp only [sub_eq_add_neg, differentiableAt_add_const_iff]
#align differentiable_at_sub_const_iff differentiableAt_sub_const_iff
+@[fun_prop]
theorem DifferentiableOn.sub_const (hf : DifferentiableOn π f s) (c : F) :
DifferentiableOn π (fun y => f y - c) s := fun x hx => (hf x hx).sub_const c
#align differentiable_on.sub_const DifferentiableOn.sub_const
@@ -580,6 +630,7 @@ theorem differentiableOn_sub_const_iff (c : F) :
simp only [sub_eq_add_neg, differentiableOn_add_const_iff]
#align differentiable_on_sub_const_iff differentiableOn_sub_const_iff
+@[fun_prop]
theorem Differentiable.sub_const (hf : Differentiable π f) (c : F) :
Differentiable π fun y => f y - c := fun x => (hf x).sub_const c
#align differentiable.sub_const Differentiable.sub_const
@@ -599,6 +650,7 @@ theorem fderiv_sub_const (c : F) : fderiv π (fun y => f y - c) x = fderiv
simp only [sub_eq_add_neg, fderiv_add_const]
#align fderiv_sub_const fderiv_sub_const
+@[fun_prop]
theorem HasStrictFDerivAt.const_sub (hf : HasStrictFDerivAt f f' x) (c : F) :
HasStrictFDerivAt (fun x => c - f x) (-f') x := by
simpa only [sub_eq_add_neg] using hf.neg.const_add c
@@ -609,16 +661,19 @@ theorem HasFDerivAtFilter.const_sub (hf : HasFDerivAtFilter f f' x L) (c : F) :
simpa only [sub_eq_add_neg] using hf.neg.const_add c
#align has_fderiv_at_filter.const_sub HasFDerivAtFilter.const_sub
+@[fun_prop]
nonrec theorem HasFDerivWithinAt.const_sub (hf : HasFDerivWithinAt f f' s x) (c : F) :
HasFDerivWithinAt (fun x => c - f x) (-f') s x :=
hf.const_sub c
#align has_fderiv_within_at.const_sub HasFDerivWithinAt.const_sub
+@[fun_prop]
nonrec theorem HasFDerivAt.const_sub (hf : HasFDerivAt f f' x) (c : F) :
HasFDerivAt (fun x => c - f x) (-f') x :=
hf.const_sub c
#align has_fderiv_at.const_sub HasFDerivAt.const_sub
+@[fun_prop]
theorem DifferentiableWithinAt.const_sub (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => c - f y) s x :=
(hf.hasFDerivWithinAt.const_sub c).differentiableWithinAt
@@ -630,6 +685,7 @@ theorem differentiableWithinAt_const_sub_iff (c : F) :
simp [sub_eq_add_neg]
#align differentiable_within_at_const_sub_iff differentiableWithinAt_const_sub_iff
+@[fun_prop]
theorem DifferentiableAt.const_sub (hf : DifferentiableAt π f x) (c : F) :
DifferentiableAt π (fun y => c - f y) x :=
(hf.hasFDerivAt.const_sub c).differentiableAt
@@ -640,6 +696,7 @@ theorem differentiableAt_const_sub_iff (c : F) :
DifferentiableAt π (fun y => c - f y) x β DifferentiableAt π f x := by simp [sub_eq_add_neg]
#align differentiable_at_const_sub_iff differentiableAt_const_sub_iff
+@[fun_prop]
theorem DifferentiableOn.const_sub (hf : DifferentiableOn π f s) (c : F) :
DifferentiableOn π (fun y => c - f y) s := fun x hx => (hf x hx).const_sub c
#align differentiable_on.const_sub DifferentiableOn.const_sub
@@ -649,6 +706,7 @@ theorem differentiableOn_const_sub_iff (c : F) :
DifferentiableOn π (fun y => c - f y) s β DifferentiableOn π f s := by simp [sub_eq_add_neg]
#align differentiable_on_const_sub_iff differentiableOn_const_sub_iff
+@[fun_prop]
theorem Differentiable.const_sub (hf : Differentiable π f) (c : F) :
Differentiable π fun y => c - f y := fun x => (hf x).const_sub c
#align differentiable.const_sub Differentiable.const_sub
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.
@@ -25,7 +25,8 @@ This file contains the usual formulas (and existence assertions) for the derivat
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.
@@ -123,9 +123,9 @@ nonrec theorem HasStrictFDerivAt.add (hf : HasStrictFDerivAt f f' x)
abel
#align has_strict_fderiv_at.add HasStrictFDerivAt.add
-nonrec theorem HasFDerivAtFilter.add (hf : HasFDerivAtFilter f f' x L)
+theorem HasFDerivAtFilter.add (hf : HasFDerivAtFilter f f' x L)
(hg : HasFDerivAtFilter g g' x L) : HasFDerivAtFilter (fun y => f y + g y) (f' + g') x L :=
- (hf.add hg).congr_left fun _ => by
+ .of_isLittleO <| (hf.isLittleO.add hg.isLittleO).congr_left fun _ => by
simp only [LinearMap.sub_apply, LinearMap.add_apply, map_sub, map_add, add_apply]
abel
#align has_fderiv_at_filter.add HasFDerivAtFilter.add
@@ -337,7 +337,7 @@ theorem HasStrictFDerivAt.sum (h : β i β u, HasStrictFDerivAt (A i) (A' i) x
theorem HasFDerivAtFilter.sum (h : β i β u, HasFDerivAtFilter (A i) (A' i) x L) :
HasFDerivAtFilter (fun y => β i in u, A i y) (β i in u, A' i) x L := by
- dsimp [HasFDerivAtFilter] at *
+ simp only [hasFDerivAtFilter_iff_isLittleO] at *
convert IsLittleO.sum h
simp [ContinuousLinearMap.sum_apply]
#align has_fderiv_at_filter.sum HasFDerivAtFilter.sum
Nsmul
-> NSMul
, Zpow
-> ZPow
, etc (#9067)
Normalising to naming convention rule number 6.
@@ -53,7 +53,7 @@ variable {s t : Set E}
variable {L Lβ Lβ : Filter E}
-section ConstSmul
+section ConstSMul
variable {R : Type*} [Semiring R] [Module R F] [SMulCommClass π R F] [ContinuousConstSMul R F]
@@ -109,7 +109,7 @@ theorem fderiv_const_smul (h : DifferentiableAt π f x) (c : R) :
(h.hasFDerivAt.const_smul c).fderiv
#align fderiv_const_smul fderiv_const_smul
-end ConstSmul
+end ConstSMul
section Add
@@ -541,6 +541,12 @@ nonrec theorem HasFDerivAt.sub_const (hf : HasFDerivAt f f' x) (c : F) :
hf.sub_const c
#align has_fderiv_at.sub_const HasFDerivAt.sub_const
+theorem hasStrictFDerivAt_sub_const {x : F} (c : F) : HasStrictFDerivAt (Β· - c) (id π F) x :=
+ (hasStrictFDerivAt_id x).sub_const c
+
+theorem hasFDerivAt_sub_const {x : F} (c : F) : HasFDerivAt (Β· - c) (id π F) x :=
+ (hasFDerivAt_id x).sub_const c
+
theorem DifferentiableWithinAt.sub_const (hf : DifferentiableWithinAt π f s x) (c : F) :
DifferentiableWithinAt π (fun y => f y - c) s x :=
(hf.hasFDerivWithinAt.sub_const c).differentiableWithinAt
@@ -663,4 +669,3 @@ theorem fderiv_const_sub (c : F) : fderiv π (fun y => c - f y) x = -fderiv
end Sub
end
-
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -31,15 +31,15 @@ noncomputable section
section
-variable {π : Type _} [NontriviallyNormedField π]
+variable {π : Type*} [NontriviallyNormedField π]
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace π E]
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace π E]
-variable {F : Type _} [NormedAddCommGroup F] [NormedSpace π F]
+variable {F : Type*} [NormedAddCommGroup F] [NormedSpace π F]
-variable {G : Type _} [NormedAddCommGroup G] [NormedSpace π G]
+variable {G : Type*} [NormedAddCommGroup G] [NormedSpace π G]
-variable {G' : Type _} [NormedAddCommGroup G'] [NormedSpace π G']
+variable {G' : Type*} [NormedAddCommGroup G'] [NormedSpace π G']
variable {f fβ fβ g : E β F}
@@ -55,7 +55,7 @@ variable {L Lβ Lβ : Filter E}
section ConstSmul
-variable {R : Type _} [Semiring R] [Module R F] [SMulCommClass π R F] [ContinuousConstSMul R F]
+variable {R : Type*} [Semiring R] [Module R F] [SMulCommClass π R F] [ContinuousConstSMul R F]
/-! ### Derivative of a function multiplied by a constant -/
@@ -326,7 +326,7 @@ section Sum
open BigOperators
-variable {ΞΉ : Type _} {u : Finset ΞΉ} {A : ΞΉ β E β F} {A' : ΞΉ β E βL[π] F}
+variable {ΞΉ : Type*} {u : Finset ΞΉ} {A : ΞΉ β E β F} {A' : ΞΉ β E βL[π] F}
theorem HasStrictFDerivAt.sum (h : β i β u, HasStrictFDerivAt (A i) (A' i) x) :
HasStrictFDerivAt (fun y => β i in u, A i y) (β i in u, A' i) x := by
@@ -2,15 +2,12 @@
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, SΓ©bastien GouΓ«zel, Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.calculus.fderiv.add
-! 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.Linear
import Mathlib.Analysis.Calculus.FDeriv.Comp
+#align_import analysis.calculus.fderiv.add from "leanprover-community/mathlib"@"e3fb84046afd187b710170887195d50bada934ee"
+
/-!
# Additive operations on derivatives
The unported dependencies are
algebra.order.module
init.core
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
algebra.order.monoid.cancel.basic
init.data.list.default
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file