theorem
  for E being finite non empty set, A,B being Event of E st prob(B) = 0
  holds A, B are_independent
proof
  let E be finite non empty set, A,B be Event of E;
  assume
A1: prob(B) = 0;
  then prob(A /\ B) <= 0 by Th19,XBOOLE_1:17;
  then prob(A /\ B) = 0 by Th18;
  hence thesis by A1;
end;
