injective_iff_bijective — Mathlib

English

For f: α → α and an equivalence e: α ≃ β, Injective f is equivalent to Bijective f (via transport along e).

Русский

Для f: α → α и эквиваленции e: α ≃ β, инъективность f эквивалентна биективности f (через перенос по e).

LaTeX

$$$\\text{Injective}(f) \\iff \\text{Bijective}(f)$$$

Lean4

theorem injective_iff_bijective {f : α → α} : Injective f ↔ Bijective f := by simp [Bijective, injective_iff_surjective]

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