filter_curry — Mathlib

English

Filtering on the first coordinate commutes with curry: (f.filter (fun a => p a.1)).curry = f.curry.filter p.

Русский

Фильтрация по первой координате commuting с каррированием: (f.filter (fun a => p a.1)).curry = f.curry.filter p.

LaTeX

$$$\bigl(f.filter(\lambda a:\<|...|\> a.1)\bigr)^{\text{curry}} = f^{\text{curry}}.filter p$$$

Lean4

theorem filter_curry (f : α × β →₀ M) (p : α → Prop) [DecidablePred p] :
    (f.filter fun a : α × β => p a.1).curry = f.curry.filter p :=
  by
  ext a b
  simp [filter_apply, apply_ite (DFunLike.coe · b)]

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