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Specification int-basic1
specification
   

   sorts int;
   
   functions  . +1 : int → int;
              . -1 : int → int;
   predicates  . < . : int × int;
   
   variables  i : int;
              i0 : int;
              j : int;
              j0 : int;
   
   

   induction int generated by 0, +1, -1;

   axioms succpred :  ⊦ i +1 -1 = i;
          used for: s, ls;
          predsucc :  ⊦ i -1 +1 = i;
          used for: s, ls;
          irref :  ⊦ ¬ i < i;
          used for: s, ls;
          trans :  ⊦ i < j ∧ j < j0 → i < j0;
          used for: f, lf;
          lsrec :  ⊦ i < j ↔ i +1 = j ∨ i +1 < j;
          lssucc :  ⊦ i +1 < j ↔ i < j -1;

   

   
end specification