proposition: Lemma umall2_sym : Symmetric P -> Symmetric um_all2.
proof: Proof. by move=>S x y; split=>H k; apply/Symmetric_optionR. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path bigop) pcm(options prelude finmap seqperm pred seqext) pcm(pcm morphism)