proposition: Lemma lte_mul_pinfty x y : 0 <= x -> x \is a fin_num -> y < +oo -> x * y < +oo.
proof: Proof. move: x y => [x| |] [y| |] // x0 xfin _; first by rewrite -EFinM ltry. rewrite mulr_infty; move: x0; rewrite lee_fin le_eqVlt => /predU1P[<-|x0]. - by rewrite sgr0 mul0e ltry. - by rewrite gtr0_sg // mul1e. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra) signed