proposition: Lemma pperm_cat_cons x s1 s2 t1 t2 : perm (s1 ++ x :: t1) (s2 ++ x :: t2) <-> perm (s1 ++ t1) (s2 ++ t2).
proof: Proof. split=>[|H]; first by apply: pperm_cat_consR. apply: (@pperm_trans (x::s1++t1))=>//; apply: (@pperm_trans (x::s2++t2))=>//. by apply/pperm_cons. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat seq path eqtype) pcm(options pred)