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Specification nat-basic
specification
   

   

   

   

   data types nat = 0
                  | . +1(. -1 : nat)
                  ;

   variables  n : nat;
              m : nat;

   

   order predicates  . < . : nat × nat;

   
   
   functions  . + . : nat × nat → nat;
   
   
   variables  m : nat;
              n0 : nat;
   
   

   

   axioms add-base :  ⊦ n + 0 = n;
          used for: s, ls;
          add-rec :  ⊦ m + n +1 = (m + n)+1;
          used for: s, ls;
          less-total :  ⊦ n < n0 ∨ n = n0 ∨ n0 < n;

   

   
end specification