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Specification funops
specification
   functions 
       cod : (A → B) → B → Bool;
       . o . : (A → B) × (B → C) → A → C;
   
   predicates 
       inj : (A → B);
       surj : (A → B);
   
   variables 
       f : A → B;
       g : B → C;
       h : A → C;
       a : A;
       b : B;
       c : C;
   axioms 
      cod-def: cod(f)(b) ↔ (∃ a. f(a) = b);
      used for: as, ls;
      
      inj-def: inj(f) ↔ (∀ a1, a2. a1 ≠ a2 → f(a1) ≠ f(a2));
      used for: ls;
      
      surj-def: surj(f) ↔ (∀ b. ∃ a. f(a) = b);
      used for: ls;
      
      compose-def: (f o g)(a) = g(f(a));
      used for: s, ls;
   
end specification