proposition: Lemma Qpair_leP k k' n: natp k -> natp k' -> natp n -> (k <=c k' <-> (Qpair k n) <=q (Qpair k' n)).
proof: Proof. move=> kN k'N nN. symmetry;apply: (iff_trans (Qpair_le0P kN nN k'N nN)). split; first by apply:(cprod_le2r (NS_pow NS2 nN) kN k'N (@cpow2_nz n)). apply: cprod_Mleeq. Qed.
imports: mathcomp(ssreflect ssrbool eqtype ssrfun)