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 Th45:
  for E being finite non empty set, A,B being Event of E st 0 <
  prob(B) & A misses B 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: A misses B;
  prob(A, B) = 0 by A2,Th38;
  then 1 - prob(A`, B) = 0 by A1,Th40;
  hence thesis;
end;
