proposition: Lemma le_trans (x y z: T): x <= y -> y <= z -> x <= z.
proof: Proof. Proof with auto. intros xley ylez q zq r qr. destruct (QnonNeg_mid q r qr). apply (xley ((1#2)*(q+r))%Qnn)... apply (ylez q)... Qed.
imports: Coq.QArith.Qabs CoRN.model.ordfields.Qordfield CoRN.model.structures.Qpossec Coq.QArith.Qminmax Coq.setoid_ring.Ring Coq.Program.Program