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From Coq Require Import ssreflect ssrfun.
From HB Require Import structures.
HB.mixin Record AddComoid_of_TYPE A := {
zero : A;
add : A -> A -> A;
addrA : associative add;
addrC : commutative add;
add0r : left_id zero add;
}.
HB.structure Definition AddComoid := { A of AddComoid_of_TYPE A }.
HB.mixin Record Ring_of_AddComoid A of AddComoid A := {
opp : A -> A;
one : A;
mul : A -> A -> A;
addNr : left_inverse zero opp add;
mulrA : associative mul;
mul1r : left_id one mul;
mulr1 : right_id one mul;
mulrDl : left_distributive mul add;
mulrDr : right_distributive mul add;
}.
HB.factory Record Ring_of_TYPE A := {
zero : A;
one : A;
add : A -> A -> A;
opp : A -> A;
mul : A -> A -> A;
addrA : associative add;
addrC : commutative add;
add0r : left_id zero add;
addNr : left_inverse zero opp add;
mulrA : associative mul;
mul1r : left_id one mul;
mulr1 : right_id one mul;
mulrDl : left_distributive mul add;
mulrDr : right_distributive mul add;
}.
#[verbose]
HB.builders Context A (a : Ring_of_TYPE A).
HB.instance
Definition to_AddComoid_of_TYPE :=
AddComoid_of_TYPE.Build A zero add addrA addrC add0r.
HB.instance
Definition to_Ring_of_AddComoid :=
Ring_of_AddComoid.Build A _ _ _ addNr mulrA mul1r
mulr1 mulrDl mulrDr.
HB.end.
(* End change *)
HB.structure Definition Ring := { A of Ring_of_TYPE A }.
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