proposition: Lemma fcatKs (s s1 s2 : fmap) : disj s s1 && disj s s2 -> fcat s s1 = fcat s s2 -> s1 = s2.
proof: Proof. case/andP=>H1 H2. rewrite (fcatC H1) (fcatC H2); apply: fcatsK. by rewrite -!(disjC s) H1 H2. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path) pcm(options)