proposition: Lemma cancel k v1 v2 f1 f2 : valid (pts k v1 \+ f1) -> pts k v1 \+ f1 = pts k v2 \+ f2 -> [/\ v1 = v2, valid f1 & f1 = f2].
proof: Proof. move=>V' E. have: find k (pts k v1 \+ f1) = find k (pts k v2 \+ f2) by rewrite E. rewrite !findPtUn -?E //; case=>X. by rewrite -{}X in E *; rewrite -(joinxK V' E) (validE2 V'). Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path bigop) pcm(options prelude finmap seqperm pred seqext) pcm(pcm morphism)