-axiom pippo: \forall x1, x2, x3. (x1 + x2 == x3) \to
- \forall y1, y2, y3. (y1 + y2 == y3) \to
- x1 <= y1 \to x2 < y2 \to x3 < y3.
+theorem nle_nplus: ∀p, q, r. p ⊕ q ≍ r → q ≤ r.
+ intros; elim H; clear H q r; autobatch.
+qed.
+
+axiom nle_nplus_comp: ∀x1,x2,x3. x1 ⊕ x2 ≍ x3 → ∀y1,y2,y3. y1 ⊕ y2 ≍ y3 →
+ x1 ≤ y1 → x2 ≤ y2 → x3 ≤ y3.
+
+axiom nle_nplus_comp_lt_2: ∀x1,x2,x3. x1 ⊕ x2 ≍ x3 → ∀y1,y2,y3. y1 ⊕ y2 ≍ y3 →
+ x1 ≤ y1 → x2 < y2 → x3 < y3.