Canonical equiv_encModRel := defaultEncModRel equiv.
Definition type := {eq_quot equiv}.
Definition type_of of phant R := type.
Canonical rquot_quotType := [quotType of type].
Canonical rquot_eqType := [eqType of type].
Canonical rquot_choiceType := [choiceType of type].
Canonical rquot_eqQuotType := [eqQuotType equiv of type].

(* Specifications: *)
Lemma idealrBE x y : (x - y) \in kI = (x == y %[mod type]).
Canonical pi_opp_morph := PiMorph1 pi_opp.
Lemma pi_add : {morph \pi : x y / x + y >-> add x y}.
Canonical pi_add_morph := PiMorph2 pi_add.
Lemma addqA: associative add.
Canonical pi_mul_morph := PiMorph2 pi_mul.
Lemma mulqA: associative mul.
Lemma nonzero1q: one != 0.
End IDomainQuotient.