lift'_surjective — Mathlib

English

If f: α →* β is surjective, then lift' f : WithZero α →* β is surjective as well.

Русский

Если f: α →* β сюръективен, то и lift' f : WithZero α →* β сюръективен.

LaTeX

$$$ \\operatorname{Surjective}(\\mathrm{lift}' f) \\text{ if } \\operatorname{Surjective}(f). $$$

Lean4

theorem lift'_surjective {f : α →* β} (hf : Surjective f) : Surjective (lift' f) :=
  by
  intro b
  obtain ⟨a, rfl⟩ := hf b
  exact ⟨a, by simp⟩

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