
theorem
  FNegation I_WB = NegationD2
  proof
    set I = I_WB;
    set f = FNegation I;
    set g = NegationD2;
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.];
      x <= 1 by XXREAL_1:1; then
      per cases by XXREAL_0:1;
      suppose
B1:     x < 1;
        f.x = I.(x,0) by FNeg
           .= 1 by FUZIMPL1:def 22,B1,A1
           .= g.x by D2Def,B1;
        hence thesis;
      end;
      suppose
B1:     x = 1;
        f.x = I.(x,0) by FNeg
           .= 0 by A1,B1,FUZIMPL1:def 22
           .= g.x by D2Def,B1;
        hence thesis;
      end;
    end;
    hence thesis by FUNCT_2:63;
  end;
