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
  for E being finite non empty set, A,B being Event of E st 0 < prob(B)
  holds 0 <= prob(A, B)
proof
  let E be finite non empty set, A,B be Event of E;
  assume
A1: 0 < prob(B);
  0 <= prob(A /\ B) by Th18;
  hence thesis by A1;
end;
