proposition: Lemma addA : associative add.
proof: Proof. elim/quotW=> x; elim/quotW=> y; elim/quotW=> z; rewrite !piE. rewrite /addf /= !numden_Ratio ?mulf_neq0 ?domP // !mulrDl. by rewrite !mulrA !addrA ![_ * _ * \d_x]mulrAC. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(ssrAC choice tuple bigop ssralg poly polydiv) mathcomp(generic_quotient)