proposition: Lemma Rdiv_Rmult_pos_neg_Rle: forall x y z t, R0 < z -> t < R0 -> x / z <= y / t -> y * z <= x * t.
proof: Proof. intros x y z t Hz Ht Hxyzt; stepl ((z*t)*(y/t)); [|field; auto]; stepr ((z*t)*(x/z)); [|field; auto]; apply Rmult_le_compat_neg_l; auto; apply Rlt_le; auto; apply Rlt_mult_neg_pos; assumption. Qed.
imports: Coq(Reals) Coq(Lra) Coq(Fourier) Coq(Euclid) Coq(Lia)