proposition: Lemma fcatC (s1 s2 : fmap) : disj s1 s2 -> fcat s1 s2 = fcat s2 s1.
proof: Proof. rewrite /fcat. elim/fmap_ind': s2 s1=>[|k v s2 L IH] s1 /=; first by rewrite fcat_nil'. rewrite disj_ins; case/andP=>D1 D2. by rewrite fcat_ins' // -IH // seqof_ins //= -fcat_ins' ?notin_path. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path) pcm(options)