proposition: Lemma BQsum_lt2l a b c: ratp a -> ratp b -> ratp c -> (c +q a <q c +q b <-> a <q b).
proof: Proof. move => pa pb pc. apply: (iff_trans (qlt_diffP (QSs pc pa) (QSs pc pb))). apply: iff_sym;apply: (iff_trans (qlt_diffP pa pb)). by rewrite BQdiff_sum_simpl_l. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)