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Specification lexical
specification
   using lexical-param
   predicates 
       lex< : elem1 × elem2 × elem1 × elem2;
   
   variables 
       a : elem1;
       b : elem2;
       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