apply — Mathlib

English

If f is an injective open monoid homomorphism, then map f is open.

Русский

Если f инъективно открытое гомоморфизм моноидов, то map f открыто.

LaTeX

$$$\\forall f : M \\to^* N\\; (\\text{Injective}(f) \\to \\text{IsOpenMap}(f) \\to \\text{IsOpenMap}(\\mathrm{map}\\ f))$$$

Lean4

/-- See Note [custom simps projection].
  We need to specify this projection explicitly in this case,
  because it is a composition of multiple projections. -/
def apply (e : P₁ ≃ᴬ[k] P₂) : P₁ → P₂ :=
  e

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