proposition: Lemma led_addE a b c : (a + b <= c) = ((a <= c) && (b <= c)).
proof: Proof. apply/idP/idP => [ablec | /andP[]]. - by rewrite (le_trans (led_addr _ _) ablec) (le_trans (led_addl _ _) ablec). - by rewrite 2!le_def => /eqP <- /eqP <-; rewrite addrCA addrA led_addr. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype choice order) mathcomp(ssrnat bigop ssralg)