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

theorem LemmaZA:
  I is satisfying_(IP) implies I is satisfying_(I3) satisfying_(I4)
  proof
    assume
a1: I is satisfying_(IP);
A2: 0 in [.0,1.] by XXREAL_1:1;
    1 in [.0,1.] by XXREAL_1:1;
    hence thesis by a1,A2;
  end;
