proposition: Lemma path_path_algebra {σ : Signature} {A B : Algebra σ} (p q : A = B) (r : ap (issig_algebra σ)^-1 p = ap (issig_algebra σ)^-1 q) : p = q.
proof: Proof. set (e := (equiv_ap (issig_algebra σ)^-1 A B)). by apply (@equiv_inv _ _ (ap e) (Equivalences.isequiv_ap _ _)). Defined.
imports: HoTT.Utf8Minimal HoTT.Basics HoTT.Classes.implementations.ne_list HoTT.Classes.implementations.family_prod HoTT.Types HoTT.HSet HoTT.Classes.implementations.list