new theory int.Lex2

examples/programs/kmp.mlw

@@ -84,9 +84,7 @@ module KnuthMorrisPratt
   lemma next_1_0:
     forall p: array char. 1 <= length p -> is_next p 1 0
 
-  predicate lt_nat (x y: int) = 0 <= y /\ x < y
-  clone import relations.Lex with type t1 = int, type t2 = int,
-    predicate rel1 = lt_nat, predicate rel2 = lt_nat
+  use import int.Lex2
 
   (* The pattern *)
 

examples/programs/mccarthy.mlw

@@ -28,10 +28,7 @@ module McCarthy91
   axiom iter_f_0: forall x: int. iter_f 0 x = x
   axiom iter_f_s: forall k x: int. 0 < k -> iter_f k x = iter_f (k-1) (f x)
 
-  predicate lt_nat (x y: int) = 0 <= y /\ x < y
-
-  clone import relations.Lex with type t1 = int, type t2 = int,
-    predicate rel1 = lt_nat, predicate rel2 = lt_nat
+  use import int.Lex2
 
   let f91_nonrec (n0: int) =
     { }

examples/programs/mccarthy/why3session.xml

@@ -17,12 +17,12 @@
      <result status="valid" time="0.01"/>
     </proof>
    </goal>
-   <goal name="WP_parameter f91_nonrec" expl="correctness of parameter f91_nonrec" sum="75f22cdba2f4a634d9942900b5b0c525" proved="true" expanded="true">
+   <goal name="WP_parameter f91_nonrec" expl="correctness of parameter f91_nonrec" sum="fbd734e7f0f402db73a779f18601e0e7" proved="true" expanded="true">
     <proof prover="alt-ergo" timelimit="2" edited="" obsolete="false">
-     <result status="valid" time="0.64"/>
+     <result status="valid" time="0.96"/>
     </proof>
     <proof prover="z3" timelimit="2" edited="" obsolete="false">
-     <result status="valid" time="0.02"/>
+     <result status="valid" time="0.04"/>
     </proof>
    </goal>
   </theory>

theories/int.why

@@ -30,6 +30,17 @@ theory MinMax
 
 end
 
+theory Lex2
+
+  use import Int
+
+  predicate lt_nat (x y: int) = 0 <= y /\ x < y
+
+  clone export relations.Lex with type t1 = int, type t2 = int,
+    predicate rel1 = lt_nat, predicate rel2 = lt_nat
+
+end
+
 theory EuclideanDivision
 
   use import Int