proposition: Lemma perm_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: perm_cat_consR. apply: (@perm_trans (x::s1++t1))=>//; apply: (@perm_trans (x::s2++t2))=>//. by apply/perm_cons. Qed.
imports: mathcomp(ssreflect ssrfun seq) LemmaOverloading(rels)