proposition: Lemma pperm_catC s1 s2 : perm (s1 ++ s2) (s2 ++ s1).
proof: Proof. elim: s1 s2=>[|x s1 IH1] s2 /=; first by rewrite cats0. apply: (@pperm_trans (x::s2++s1)); first by apply: permutation_skip. elim: s2=>[|y s2 IH2] //=. apply: (@pperm_trans (y::x::s2++s1)); first by apply: permutation_swap. by apply: permutation_skip. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat seq path eqtype) pcm(options pred)