Specification int-basic1

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specification
   sorts Int;
   functions 
       . +1 : Int → Int;
       . -1 : Int → Int;
   
   predicates 
       . < . : Int × Int;
   
   variables 
       i : Int;
       j : Int;
   induction 
      Int generated by 0,  . +1 : (Int → Int),  . -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