[Imprint][Data Privacy Statement][E-Mail]

Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

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