Definition is_aspace U := has_algid U && (U * U <= U)%VS.Structure aspace := ASpace {asval :> {vspace aT}; _ : is_aspace asval}.Structure aspace := ASpace {asval :> {vspace aT}; _ : is_aspace asval}.Structure aspace := ASpace {asval :> {vspace aT}; _ : is_aspace asval}.Definition aspace_of of phant aT := aspace.Notation "''AEnd' ( aT )" := (ahom aT aT) : type_scope.Canonical aspace_eqType := Eval hnf in EqType aspace aspace_eqMixin.Canonical aspace_choiceType := Eval hnf in ChoiceType aspace aspace_choiceMixin.Fact aspace1_subproof : is_aspace 1.Canonical aspace1 : {aspace aT} := ASpace aspace1_subproof.

Lemma aspacef_subproof : is_aspace fullv.