Theorems · Theorem · global analysis

LineDifferentiableWithinAt.congr_mono

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {E : Type u_3} [inst_3 : AddCommGroup E] [inst_4 : Module 𝕜 E] {f f₁ : E → F} {s t : Set E}
  {x v : E},
  LineDifferentiableWithinAt 𝕜 f s x v → Set.EqOn f₁ f t → f₁ x = f x → t ⊆ s → LineDifferentiableWithinAt 𝕜 f₁ t x v

Defined in

Mathlib.Analysis.Calculus.LineDeriv.Basic

Cited by

1 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceAddCommGroupModule