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;
