theorem Th41:
  for E being finite non empty set, A,B being Event of E st 0 <
  prob(B) & B c= A holds prob(A, B) = 1
proof
  let E be finite non empty set, A,B be Event of E;
  assume that
A1: 0 < prob(B) and
A2: B c= A;
  prob(A /\ B) = prob(B) by A2,XBOOLE_1:28;
  hence thesis by A1,XCMPLX_1:60;
end;
