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From HB Require Import structures.
From Coq Require Import ssreflect ssrfun.
HB.mixin Record MulMonoid_of_Type A := {
one : A;
mul : A -> A -> A;
mulrA : associative mul;
mul1r : left_id one mul;
mulr1 : right_id one mul;
}.
HB.structure Definition MulMonoid := { A of MulMonoid_of_Type A }.
HB.mixin Record Ring_of_MulMonoid A of MulMonoid A := {
zero : A;
add : A -> A -> A;
addrA : associative add;
add0r : left_id zero add;
addr0 : right_id zero add;
opp : A -> A;
addrC : commutative (add : A -> A -> A);
addNr : left_inverse zero opp add;
mulrDl : left_distributive mul add;
mulrDr : right_distributive mul add;
}.
HB.structure Definition Ring := { A of MulMonoid A & Ring_of_MulMonoid A }.
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