cancel_right — Mathlib

English

For any f, composing with the identity on the right yields f itself.

Русский

Любой f, композиция с идентичностью справа даёт сам f.

LaTeX

$$$\\forall f:\\mathrm{BoundedLatticeHom}(\\alpha, \\beta):\\ (\\mathrm{BoundedLatticeHom.id}\\,\\beta).\\mathrm{comp}\\ f = f$$$

Lean4

@[simp]
theorem cancel_right {g₁ g₂ : BoundedLatticeHom β γ} {f : BoundedLatticeHom α β} (hf : Surjective f) :
    g₁.comp f = g₂.comp f ↔ g₁ = g₂ :=
  ⟨fun h => BoundedLatticeHom.ext <| hf.forall.2 <| DFunLike.ext_iff.1 h, fun h => congr_arg₂ _ h rfl⟩

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