- system flag now forks for matitadep too

[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 7bcdd6010b05216352e85f093c2f35d68d208f5c..d90adb92627ddcc8bdb08c939b30d8a802bb3421 100644 (file)
--- a/helm/software/matita/contribs/RELATIONAL/NLE/nplus.ma
+++ b/helm/software/matita/contribs/RELATIONAL/NLE/nplus.ma
@@ -16,6 +16,14 @@ set "baseuri" "cic:/matita/RELATIONAL/NLE/nplus".
 
 include "NLE/defs.ma".
 
-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: \forall p, q, r. (p + q == r) \to 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_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.