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Specification lexical
specification
   

   

   

   using lexical-param


   

   

   

   

   
   
   
   predicates  lex< : elem1 × elem2 × elem1 × elem2;
   
   variables  IHPQ : elem1 × elem2 → bool;
   
   

   

   axioms lex-def :  ⊦ lex<(a0, b0, a, b) ↔ a0 ≪1 a ∨ a0 = a ∧ b0 ≪2 b;

   theorems lexirrefl :  ⊦ ¬ lex<(a, b, a, b);
            used for: s, ls;
            lextrans :  ⊦ lex<(a, b, a0, b0) ∧ lex<(a0, b0, a1, b1) → lex<(a, b, a1, b1);
            used for: f, lf;
            wflex : ∀ a, b. (∀ a0, b0. lex<(a0, b0, a, b) → IHPQ(a0, b0)) → IHPQ(a, b) ⊦ IHPQ(a, b);

   
end specification