proposition: Fact pair_addN : left_inverse (0, 0) opp_pair (@add_pair U V).
proof: Proof. by move=> x; congr (_, _); apply: addNr. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)