English
The map prodComparison between L A and B is an isomorphism; its inverse is given by the other direction of the bijection evaluated at the identity.
Русский
Координационная карта prodComparison между LA и LB является изоморфизмом; её обратное отображение задаётся другой стороной биекции на тождестве.
LaTeX
$$$ \\text{IsIso}(\\mathrm{prodComparison}(\\reflector i)\\; A\\; B) $$$
Lean4
/-- The bijection allows us to show that `prodComparison L A B` is an isomorphism, where the inverse
is the forward map of the identity morphism.
-/
theorem prodComparison_iso (A B : C) : IsIso (prodComparison (reflector i) A B) :=
⟨⟨bijection i _ _ _ (𝟙 _), by
rw [← (bijection i _ _ _).injective.eq_iff, bijection_natural, ← bijection_symm_apply_id, Equiv.apply_symm_apply,
id_comp],
by rw [← bijection_natural, id_comp, ← bijection_symm_apply_id, Equiv.apply_symm_apply]⟩⟩
