gciMapComap — Mathlib

English

The comap map is strictly monotone when f is surjective (repeat).

Русский

The comap map is strictly monotone when f is surjective (repeat).

LaTeX

$$StrictMono (comap f)$$

Lean4

/-- `map f` and `comap f` form a `GaloisCoinsertion` when `f` is injective. -/
def gciMapComap (hf : Injective f) : GaloisCoinsertion (map f) (comap f) :=
  (gc_map_comap f).toGaloisCoinsertion fun S x =>
    by
    simp only [mem_comap, mem_map, forall_exists_index, and_imp]
    intro y hy hxy
    rw [hf.eq_iff] at hxy
    rwa [← hxy]

Похожие утверждения