proposition: Lemma muln_snum_subproof (xnz ynz : nullity) (xr yr : reality) (x : {compare 0 & xnz & xr}) (y : {compare 0 & ynz & yr}) (rnz := mul_nonzero_subdef xnz ynz xr yr) (rrl := mul_reality_subdef xnz ynz xr yr) : Signed.spec 0 rnz rrl (x%:num * y%:num).
proof: Proof. rewrite {}/rnz {}/rrl; apply/andP; split; move: xr yr xnz ynz x y => [[[]|]|] [[[]|]|] [] []//=; by move=> [[|x]//= _] [[|y]//= _]; rewrite muln0. Qed.
imports: HB(structures) Coq(ssreflect ssrfun ssrbool) mathcomp(ssrnat eqtype choice order ssralg ssrnum ssrint) mathcomp(mathcomp_extra)