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Specification int-basic1
specification
   sorts int;
   functions 
       . +1 : int → int;
       . -1 : int → int;
   
   predicates 
       . < . : int × int;
   
   variables 
       i : int;
       j : 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