English
A variant statement of the Five Lemma in the module context with similar hypotheses implies the middle map is bijective.
Русский
Вариант Пятой леммы в контексте модулей с аналогичными предпосылками даёт биективность центрального отображения.
LaTeX
$$$$\text{(Same structure as 6853 with adjusted hypotheses) } \Rightarrow \operatorname{Bijective}(i_3).$$$$
Lean4
/-- Pullback a multiplicative distributive multiplicative action along an injective monoid
homomorphism. -/
-- See note [reducible non-instances]
protected abbrev mulDistribMulAction [Monoid B] [SMul M B] (f : B →* A) (hf : Injective f)
(smul : ∀ (c : M) (x), f (c • x) = c • f x) : MulDistribMulAction M B
where
__ := hf.mulAction f smul
smul_mul c x y := hf <| by simp only [smul, f.map_mul, smul_mul']
smul_one c := hf <| by simp only [smul, f.map_one, smul_one]
