proposition: Lemma BQsum_Mlele a b c d: a <=q c -> b <=q d -> (a +q b) <=q (c +q d).
proof: Proof. move => eq1 eq2; move: (proj32 eq1) (proj31 eq2)=> cz bz. move /(BQsum_le2r (proj31 eq1) cz bz): eq1 => eq3. move/(BQsum_le2l bz (proj32 eq2) cz): eq2 => eq4. BQo_tac. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)