
theorem Prop1417ii: :: Proposition 1.4.17 ii)
  for I being satisfying_(EP) satisfying_(OP) BinOp of [.0,1.]
  for x being Element of [.0,1.] holds
      x <= (FNegation I).((FNegation I).x)
  proof
    let I be satisfying_(EP) satisfying_(OP) BinOp of [.0,1.];
    let x be Element of [.0,1.];
    set f = FNegation I;
A1: 0 in [.0,1.] by XXREAL_1:1;
    f.x in [.0,1.]; then
A2: I.(x,0) in [.0,1.] by FNeg; then
a7: I.(x,(I.(I.(x,0),0))) = I.(I.(x,0),I.(x,0)) by A1,FUZIMPL2:def 2
         .= 1 by A2,FUZIMPL2:def 3;
    I.(I.(x,0),0) = I.(f.x,0) by FNeg
                 .= f.(f.x) by FNeg;
    hence thesis by a7,FUZIMPL2:def 4;
  end;
