proposition: Lemma equivalence_relP : equivalence_rel <-> reflexive /\ left_transitive.
proof: Proof. split=> [eqiR | [Rxx trR] x y z]; last by split=> [|/trR->]. by split=> [x | x y Rxy z]; [rewrite (eqiR x x x) | rewrite (eqiR x y z)]. Qed.
imports: ssreflect ssrfun