English
The exactness of inr and fst is a basic example of a direct sum decomposition.
Русский
Точность inr и fst — базовый пример разложения в прямую сумму.
LaTeX
$$$$ \\operatorname{Exact}(\\mathrm{inr},\\mathrm{fst}). $$$$
Lean4
theorem inl_snd : Function.Exact (LinearMap.inl R M N) (LinearMap.snd R M N) :=
by
rintro ⟨x, y⟩
simp only [LinearMap.snd_apply, @eq_comm _ y, LinearMap.coe_inl, Set.mem_range, Prod.mk.injEq, exists_eq_left]