
theorem Lemma154iv:
  for I being BinOp of [.0,1.],    :: for Fuzzy_Implication it is trivial
      N being Fuzzy_Negation st
    I is satisfying_(RB) N-satisfying_CP holds
      I is satisfying_(LB)
  proof
    let I be BinOp of [.0,1.],
        N be Fuzzy_Negation;
    assume that
A1: I is satisfying_(RB) and
A2: I is N-satisfying_CP;
    let y be Element of [.0,1.];
A4: 0 in [.0,1.] by XXREAL_1:1;
A3: N.0 = 1 by FUZIMPL3:def 4;
    I.(0,y) = I.(N.y,N.0) by A2,A4
           .= 1 by A1,A3;
    hence thesis;
  end;
