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+Require Import Reals.
+Require Import Lra.
+
+Open Scope R_scope.
+
+Lemma l1 : forall x y z : R, Rabs (x - z) <= Rabs (x - y) + Rabs (y - z).
+intros; split_Rabs; lra.
+Qed.
+
+Lemma l2 :
+ forall x y : R, x < Rabs y -> y < 1 -> x >= 0 -> - y <= 1 -> Rabs x <= 1.
+intros.
+split_Rabs; lra.
+Qed.