proposition: Lemma weird_triangleIR : forall x y, AbsIR x[-]AbsIR (y[-]x) [<=] AbsIR y.
proof: Proof. intros. apply shift_minus_leEq. simpl in |- *; unfold ABSIR in |- *; apply Max_leEq. rstepl (y[+][--] (y[-]x)). apply plus_resp_leEq_both; [ apply lft_leEq_Max | apply rht_leEq_Max ]. rstepl ( [--]y[+] (y[-]x)). apply plus_resp_leEq_both; [ apply rht_leEq_Max | apply lft_leEq_Max ]. Qed.
imports: CoRN.reals.OddPolyRootIR