proposition: Lemma domeq2P (f1 : U1) (f2 : U2) : reflect (valid f1 = valid f2 /\ dom f1 = dom f2) (dom_eq2 f1 f2).
proof: Proof. by rewrite /dom_eq2; apply/andPP/eqP/eqP. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path bigop) pcm(options prelude finmap seqperm pred seqext) pcm(pcm morphism)