removing old contribs

[helm.git] / helm / software / matita / contribs / RELATIONAL / NLE / nplus.ma

diff --git a/helm/software/matita/contribs/RELATIONAL/NLE/nplus.ma b/helm/software/matita/contribs/RELATIONAL/NLE/nplus.ma
index 85dac01a9d92e62cfaf0becd52797ef3878875df..22998c0385b9e1246aa02921c431e9a4439567f9 100644 (file)
--- a/helm/software/matita/contribs/RELATIONAL/NLE/nplus.ma
+++ b/helm/software/matita/contribs/RELATIONAL/NLE/nplus.ma
@@ -16,14 +16,12 @@
 
 include "NLE/defs.ma".
 
-theorem nle_nplus: \forall p, q, r. (p + q == r) \to q <= r.
- intros. elim H; clear H q r; autobatch.
+theorem nle_nplus: ∀p, q, r. p ⊕ q ≍ r → q ≤ r.
+ intros; elim H; clear H q r; autobatch.
 qed.
 
-axiom nle_nplus_comp: \forall x1, x2, x3. (x1 + x2 == x3) \to
-                      \forall y1, y2, y3. (y1 + y2 == y3) \to
-                      x1 <= y1 \to x2 <= y2 \to x3 <= y3.
+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: \forall x1, x2, x3. (x1 + x2 == x3) \to
-                           \forall y1, y2, y3. (y1 + y2 == y3) \to
-                           x1 <= y1 \to x2 < y2 \to 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.