
theorem CoIn01:
  for f being BinOp of [.0,1.],
      a, b being Real holds
   1 - f.(1 - a, 1 - b) in [.0,1.]
  proof
    let f be BinOp of [.0,1.];
    let a,b be Real;
    per cases;
    suppose a in [.0,1.] & b in [.0,1.]; then
      reconsider aa = a, bb = b as Element of [.0,1.];
      f.(1-aa, 1-bb) in [.0,1.] by NormIn01;
      hence thesis by OpIn01;
    end;
    suppose not a in [.0,1.] or not b in [.0,1.];
      f.(1-a,1-b) in [.0,1.] by NormIn01;
      hence thesis by OpIn01;
    end;
  end;
