proposition: Theorem cover_comp {x y z w v u : C} (f : y ~> z) (h : x ~> y) (g : v ~> u) (i : w ~> v) : cover f g ∘ cover h i ≈ cover (f ∘ h) (g ∘ i).
proof: Proof. unmerge. rewrite !comp_assoc. rewrite <- merge_comp. unfold cover. 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