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)]