
theorem Th15:
  for A be set, B be non empty set,
  b being Element of B, f being bifunction of A,B st f = [:A,A:] --> [b,b]
  holds f is Covariant Contravariant
proof
  let A be set, B be non empty set,
  b be Element of B, f be bifunction of A,B such that
A1: f = [:A,A:] --> [b,b];
  reconsider g = A --> b as Function of A,B;
  thus f is Covariant
  proof
    take g;
    thus thesis by A1,ALTCAT_2:1;
  end;
  take g;
  [:A,A:] --> [b,b] = ~([:A,A:] --> [b,b]) by Th5;
  hence thesis by A1,ALTCAT_2:1;
end;
