cancel_right — Mathlib

English

cancel_right: if f is surjective, g1 ∘ f = g2 ∘ f implies g1 = g2.

Русский

cancel_right: если f сюръективен, то g1∘f = g2∘f тогда и только тогда g1 = g2.

LaTeX

$$$\\operatorname{Surjective}(f) \\Rightarrow (g_1\\circ f = g_2\\circ f \\iff g_1 = g_2)$$$

Lean4

@[simp]
theorem cancel_right {g₁ g₂ : EsakiaHom β γ} {f : EsakiaHom 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 (comp · f)⟩

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