proposition: Lemma setIrel_equivalence z: (alls z equivalence) -> equivalence (intersection z).
proof: Proof. move=> alleq; apply: symmetric_transitive_equivalence. - by apply: setIrel_graph => r /alleq []. - by apply: setIrelS=> // r /alleq [_ _]. - by apply: setIrelT=> // r /alleq [_ _ ]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)