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 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;
