
theorem Lemma15312:
  for I being BinOp of [.0,1.],
      N being negation-strong Fuzzy_Negation holds
   I is N-satisfying_CP implies
     I is N-satisfying_L-CP
  proof
    let I be BinOp of [.0,1.],
        N be negation-strong Fuzzy_Negation;
    assume
a0: I is N-satisfying_CP;
d1: N is involutive by FUZIMPL3:def 11,def 13;
    for x,y being Element of [.0,1.] holds
      I.(N.x,y) = I.(N.y,x)
    proof
      let x,y be Element of [.0,1.];
      I.(N.x,y) = I.(N.y,N.(N.x)) by a0
               .= I.(N.y,x) by d1,FUZIMPL3:def 8;
      hence thesis;
    end;
    hence thesis;
  end;
