Module Type PermDefSig.
Parameter fun_of_perm : forall T, perm_type T -> T -> T.
Parameter perm : forall (T : finType) (f : T -> T), injective f -> {perm T}.

Axiom fun_of_permE : fun_of_perm = fun_of_perm_def.
Axiom permE : perm = perm_def.