
theorem
  FNegation I_LK = N_CC
  proof
    set I = I_LK;
    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 <= 1 by XXREAL_1:1;
      f.x = I.(x,0) by FNeg
         .= min (1,1-x+0) by A1,FUZIMPL1:def 14
         .= 1 - x by A2,XXREAL_0:def 9
         .= g.x by NDef;
      hence thesis;
    end;
    hence thesis by FUNCT_2:63;
  end;
