cancel_right — Mathlib

English

Same cancellation principle for FrameHom with right composition under surjectivity.

Русский

Та же принцип отмены для FrameHom с правой композицией при сюръективности.

LaTeX

$$Same as above: surjective f implies (g1.comp f = g2.comp f) ↔ g1 = g2.$$

Lean4

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

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