proposition: Fact lt0_add x y : 0 < x -> 0 < y -> 0 < x + y.
proof: Proof. rewrite !lt_def => /andP [x_neq0 l0x] /andP [y_neq0 l0y]; rewrite le0_add //. rewrite andbT addr_eq0; apply: contraNneq x_neq0 => hxy. by rewrite [x](@le0_anti) // hxy -le0N opprK. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)