Definition perm_of_baseFinGroupMixin : FinGroup.mixin_of (perm_type T) :=
  FinGroup.Mixin perm_mulP perm_oneP perm_invP.Canonical perm_baseFinGroupType :=
  Eval hnf in BaseFinGroupType (perm_type T) perm_of_baseFinGroupMixin.Canonical perm_finGroupType := @FinGroupType perm_baseFinGroupType perm_invP.

Lemma perm_onM H s t : perm_on H s -> perm_on H t -> perm_on H (s * t).