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