
theorem FNegI3:
  FNegation I_I3 = NegationD1
  proof
    set I = I_I3;
    set f = FNegation I;
    set g = NegationD1;
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.];
      per cases;
      suppose
B1:     x = 0;
        f.x = I.(x,0) by FUZIMPL3:def 16
           .= 1 by II3Def,B1
           .= g.x by FUZIMPL3:def 17,B1;
        hence thesis;
      end;
      suppose
B1:     x <> 0;
        f.x = I.(x,0) by FUZIMPL3:def 16
           .= 0 by A1,B1,II3Def
           .= g.x by FUZIMPL3:def 17,B1;
        hence thesis;
      end;
    end;
    hence thesis by FUNCT_2:63;
  end;
