
theorem
  FNegation I_RC = N_CC
  proof
    set I = I_RC;
    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.];
      f.x = I.(x,0) by FNeg
         .= 1 - x + x * 0 by FUZIMPL1:def 17,A1
         .= g.x by NDef;
      hence thesis;
    end;
    hence thesis by FUNCT_2:63;
  end;
