Theorems · Theorem · real analysis

HasDerivWithinAt.congr_simp

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : AddCommGroup F] [inst_2 : Module 𝕜 F]
  [inst_3 : TopologicalSpace F] [inst_4 : ContinuousSMul 𝕜 F] (f f_1 : 𝕜 → F),
  f = f_1 →
    ∀ (f' f'_1 : F),
      f' = f'_1 →
        ∀ (s s_1 : Set 𝕜),
          s = s_1 → ∀ (x x_1 : 𝕜), x = x_1 → HasDerivWithinAt f f' s x = HasDerivWithinAt f_1 f'_1 s_1 x_1

Defined in

Mathlib.Analysis.Calculus.Deriv.Mul

Cited by

29 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceContinuousSMul