proposition: Theorem inbetween_bounds : inbetween l -> (d <= x < u)%R.
proof: Proof. intros [Hx|l' Hx Hl] ; clear l. rewrite Hx. split. apply Rle_refl. exact Hdu. now split ; try apply Rlt_le. Qed.
imports: Coq(ZArith Reals Lia) Zaux Raux Defs Float_prop