proposition: Lemma Rabs_middle_is_in_the_middle : forall x y, 0 <= x -> x < y -> x < Rabs (middle x y) < y.
proof: Proof. intros x y x_pos x_lt_y. assert (mxy_pos : 0 < middle x y). apply Rle_lt_trans with x ; [| apply middle_is_in_the_middle] ; assumption. rewrite Rabs_pos_eq ; [ apply middle_is_in_the_middle |] ; intuition (auto with real). Qed.
imports: Rbase Rfunctions Rfunction_def Rtopology Lra MyRIneq MyNeq PSeries_reg Tactics