proposition: Theorem left_cover {x y z v u : C} (f : y ~> z) (h : x ~> y) (g : v ~> u) : left f ∘ cover h g ≈ cover (f ∘ h) g.
proof: Proof. unmerge. rewrite <- merge_comp. rewrite !comp_assoc. rewrite inl_merge. rewrite inr_merge. reflexivity. Qed.
imports: Category.Lib Category.Theory.Category Category.Theory.Isomorphism Category.Structure.Cartesian Category.Structure.Initial Category.Construction.Opposite