subtypePerm_ofSubtype — Mathlib

English

If f is a permutation on α, then applying subtypePerm to the inclusion of f gives back f itself, i.e. subtypePerm(ofSubtype f) with the mem-mem condition equals f.

Русский

Если f перестановка на α, то subtypePerm(ofSubtype f) = f (с условием мемори) на подтипе.

LaTeX

$$$ \\operatorname{subtypePerm}(\\mathrm{ofSubtype} f) (\\mathrm{ofSubtype\\_apply\\_mem} f) = f $$$

Lean4

@[simp]
theorem subtypePerm_ofSubtype (f : Perm (Subtype p)) : subtypePerm (ofSubtype f) (ofSubtype_apply_mem_iff_mem f) = f :=
  Equiv.ext fun x => Subtype.coe_injective (ofSubtype_apply_coe f x)

Похожие утверждения