Require Export Lci.
Definition antisym (A : Set) (R : A -> A -> Prop) :=
forall x y : A, R x y -> R y x -> x = y :>A.
Definition pi1 : forall (A : Set) (P : A -> Prop), {x : A | P x} -> A.
Definition inversible (S : Set) (Mult : S -> S -> S)
(I x : S) := exists y : S, Mult x y = I /\ Mult y x = I.

(* Specifications: *)
Lemma inv_com :
forall (S : Set) (Mult : S -> S -> S) (I x : S),
commutativity S Mult ->
(exists y : S, Mult x y = I) -> inversible S Mult I x.