
theorem
  for fi being Fuzzy_Implication holds
    I_{0} <= fi
  proof
    let fi be Fuzzy_Implication;
    set f = I_{0};
    for x,y being Element of [.0,1.] holds
      f.(x,y) <= fi.(x,y)
    proof
      let x,y be Element of [.0,1.];
A0:   x >= 0 & y <= 1 by XXREAL_1:1;
      per cases;
      suppose A1: x = 0 or y = 1; then
        f.(x,y) = 1 by LBProp,RBProp;
        hence thesis by LBProp,RBProp,A1;
      end;
      suppose x <> 0 & y <> 1; then
        x > 0 & y < 1 by A0,XXREAL_0:1; then
        f.(x,y) = 0 by I0Impl;
        hence thesis by XXREAL_1:1;
      end;
    end;
    hence thesis by FUZNORM1:def 16;
  end;
