 reserve x,y for Element of [.0,1.];
 reserve I for BinOp of [.0,1.];

theorem LemmaWA:
  I is satisfying_(NP) implies I is satisfying_(I4) satisfying_(I5)
  proof
    assume
a1: I is satisfying_(NP);
    1 in [.0,1.] by XXREAL_1:1;
    hence I is satisfying_(I4) by a1;
    0 in [.0,1.] by XXREAL_1:1;
    hence thesis by a1;
  end;
