Canonical ordinalGI_eqType := Eval hnf in EqType ordinalGI ordinalGI_eqMixin.Canonical ordinalGI_choiceType :=
  Eval hnf in ChoiceType ordinalGI ordinalGI_choiceMixin.Canonical ordinalGI_countType :=
  Eval hnf in CountType ordinalGI ordinalGI_countMixin.

Lemma ordGI_inj : injective GI_of_ord.