cancel_right — Mathlib

English

If f is surjective, then g1.comp f = g2.comp f implies g1 = g2; conversely, equality of g1 and g2 implies equality after composition.

Русский

Если f сюръективно отображает, то g1 ∘ f = g2 ∘ f эквивалентно g1 = g2; иначе равенство сохраняется.

LaTeX

$$$\text{Surjective } f \Rightarrow (g_1.comp f = g_2.comp f \iff g_1 = g_2)$$$

Lean4

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

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