proposition: Lemma validFUn k f1 f2 : valid (f1 \+ f2) -> valid (free f1 k \+ f2).
proof: Proof. case: validUn=>// V1 V2 H _; case: validUn=>//; last 1 first. - by move=>k'; rewrite domF inE; case: eqP=>// _ /H/negbTE ->. by rewrite validF V1. by rewrite V2. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path bigop) pcm(options prelude finmap seqperm pred seqext) pcm(pcm morphism)