Fact aspace_divr_closed K : divr_closed K.Canonical aspace_mulrPred K := MulrPred (aspace_divr_closed K).Canonical aspace_divrPred K := DivrPred (aspace_divr_closed K).Canonical aspace_smulrPred K := SmulrPred (aspace_divr_closed K).Canonical aspace_sdivrPred K := SdivrPred (aspace_divr_closed K).Canonical aspace_semiringPred K := SemiringPred (aspace_divr_closed K).Canonical aspace_subringPred K := SubringPred (aspace_divr_closed K).Canonical aspace_subalgPred K := SubalgPred (memv_submod_closed K).Canonical aspace_divringPred K := DivringPred (aspace_divr_closed K).Canonical aspace_divalgPred K := DivalgPred (memv_submod_closed K).Canonical subvs_comRingType K :=
  Eval hnf in ComRingType (subvs_of K) (@subvs_mulC K).Canonical subvs_idomainType K :=
  Eval hnf in IdomainType (subvs_of K) (@subvs_mul_eq0 K).

Lemma subvs_fieldMixin K : GRing.Field.mixin_of (@subvs_idomainType K).