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 perm1 x : (1 : {perm T}) x = x.