Definition perm_inv s := perm (can_inj (perm_invK s)).Definition perm_mul s t := perm (inj_comp (@perm_inj t) (@perm_inj s)).

(* Specifications: *)
Lemma perm_oneP : left_id perm_one perm_mul.
Lemma perm_invP : left_inverse perm_one perm_inv perm_mul.
Lemma perm_mulP : associative perm_mul.