
theorem Lemma154vb:
  for I being BinOp of [.0,1.],    :: for Fuzzy_Implication it is trivial
      N being Fuzzy_Negation st
    I is satisfying_(NP) N-satisfying_CP holds
      I is satisfying_(I3) satisfying_(I4) satisfying_(I5)
:: I4 and I5 obtained automatically
  proof
    let I be BinOp of [.0,1.],
        N be Fuzzy_Negation;
    assume that
A1: I is satisfying_(NP) and
A2: I is N-satisfying_CP;
T1: N = FNegation I & FNegation I is negation-strong
      by A1,A2,Lemma154va;
    0 in [.0,1.] by XXREAL_1:1; then
    I.(0,0) = (FNegation I).0 by FUZIMPL3:def 16
           .= 1 by T1,FUZIMPL3:def 4;
    hence thesis by A1;
  end;
