cancel_left — Mathlib

English

If g is injective, then g ∘ f1 = g ∘ f2 implies f1 = f2.

Русский

Если g инъективен, то g ∘ f1 = g ∘ f2 ⇒ f1 = f2.

LaTeX

$$$\\text{Injective}(g)\\;\\Rightarrow\\; g\\circ f_1 = g\\circ f_2 \\iff f_1 = f_2.$$$

Lean4

@[simp]
theorem cancel_left {g : BotHom β γ} {f₁ f₂ : BotHom α β} (hg : Injective g) : g.comp f₁ = g.comp f₂ ↔ f₁ = f₂ :=
  ⟨fun h => BotHom.ext fun a => hg <| by rw [← BotHom.comp_apply, h, BotHom.comp_apply], congr_arg _⟩

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