Definition coset_of_groupMixin :=
  FinGroup.Mixin coset_mulP coset_oneP coset_invP.Canonical coset_baseGroupType :=
  Eval hnf in BaseFinGroupType coset_of coset_of_groupMixin.Canonical coset_groupType := FinGroupType coset_invP.Canonical coset_morphism := Morphism coset_morphM.Implicit Type xbar : coset_of.

Lemma coset_reprK : cancel (fun xbar => repr xbar) coset.