differentiableOn_finCons' — Mathlib

English

Variant: DifferentiableOn of Fin.cons is equivalent to differentiability of φ and φs on s.

Русский

Вариант: дифференцируемость Fin.cons на s эквивалентна дифференцируемости φ и φs на s.

LaTeX

$$$\\text{DifferentiableOn}_{\\mathbb{K}}(\\lambda x.\\mathrm{Fin.cons}(\\phi x)(\\phi_s x)) s \\iff \\text{DifferentiableOn}_{\\mathbb{K}}(\\phi) s ∧ \\text{DifferentiableOn}_{\\mathbb{K}}(\\phi_s) s$$$

Lean4

/-- A variant of `differentiableOn_finCons` where the derivative variables are free on the RHS
instead. -/
theorem differentiableOn_finCons' :
    DifferentiableOn 𝕜 (fun x => Fin.cons (φ x) (φs x)) s ↔ DifferentiableOn 𝕜 φ s ∧ DifferentiableOn 𝕜 φs s :=
  differentiableOn_finCons

Похожие утверждения