
theorem Lemma154iii:
  for I being BinOp of [.0,1.],    :: for Fuzzy_Implication it is trivial
      N being Fuzzy_Negation st
    I is satisfying_(LB) N-satisfying_CP holds
      I is satisfying_(RB)
  proof
    let I be BinOp of [.0,1.],
        N be Fuzzy_Negation;
    assume that
A1: I is satisfying_(LB) and
A2: I is N-satisfying_CP;
    let x be Element of [.0,1.];
A3: N.1 = 0 by FUZIMPL3:def 4;
    1 in [.0,1.] by XXREAL_1:1; then
    I.(x,1) = I.(N.1,N.x) by A2
           .= 1 by A1,A3;
    hence thesis;
  end;
