cancel_left — Mathlib

English

cancel_left: if g is injective, g ∘ f1 = g ∘ f2 implies f1 = f2.

Русский

cancel_left: если g инъективен, то g ∘ f1 = g ∘ f2 tức 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 : EsakiaHom β γ} {f₁ f₂ : EsakiaHom α β} (hg : Injective g) : g.comp f₁ = g.comp f₂ ↔ f₁ = f₂ :=
  ⟨fun h => ext fun a => hg <| by rw [← comp_apply, h, comp_apply], congr_arg _⟩

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