Theorems · Theorem · functional analysis

ContinuousMultilinearMap.linearDeriv.congr_simp

∀ {R : Type u} {ι : Type v} {M₁ : ι → Type w₁} {M₂ : Type w₂} [inst : Semiring R]
  [inst_1 : (i : ι) → AddCommMonoid (M₁ i)] [inst_2 : AddCommMonoid M₂] [inst_3 : (i : ι) → Module R (M₁ i)]
  [inst_4 : Module R M₂] [inst_5 : (i : ι) → TopologicalSpace (M₁ i)] [inst_6 : TopologicalSpace M₂]
  (f f_1 : ContinuousMultilinearMap R M₁ M₂),
  f = f_1 →
    ∀ [inst_7 : ContinuousAdd M₂] [inst_8 : DecidableEq ι] [inst_9 : Fintype ι] (x x_1 : (i : ι) → M₁ i),
      x = x_1 → f.linearDeriv x = f_1.linearDeriv x_1

Defined in

Mathlib.Analysis.Normed.Module.Multilinear.Basic

Cited by

1 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModuleTopologicalSpaceTopologicalSpaceContinuousAddDecidableEqFintype