reserve E for non empty set;
reserve a for Element of E;
reserve A, B for Subset of E;
reserve Y for set;
reserve p for FinSequence;
reserve e, e1, e2 for Singleton of E;

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;
