
theorem
  FNegation I_KD = N_CC
  proof
    set I = I_KD;
    set f = FNegation I;
    set g = N_CC;
A1: 0 in [.0,1.] by XXREAL_1:1;
    for x being Element of [.0,1.] holds f.x = g.x
    proof
      let x be Element of [.0,1.];
      1 - x in [.0,1.] by FUZNORM1:7; then
A2:   1 - x >= 0 by XXREAL_1:1;
      f.x = I.(x,0) by FNeg
         .= max (1 - x, 0) by FUZIMPL1:def 18,A1
         .= 1 - x by A2,XXREAL_0:def 10
         .= g.x by NDef;
      hence thesis;
    end;
    hence thesis by FUNCT_2:63;
  end;
