reserve n,m,k,i for Nat,
  g,s,t,p for Real,
  x,y,z for object, X,Y,Z for set,
  A1 for SetSequence of X,
  F1 for FinSequence of bool X,
  RFin for real-valued FinSequence,
  Si for SigmaField of X,
  XSeq,YSeq for SetSequence of Si,
  Omega for non empty set,
  Sigma for SigmaField of Omega,
  ASeq,BSeq for SetSequence of Sigma,
  P for Probability of Sigma;

theorem Th45:
  ASeq is disjoint_valued implies Partial_Sums(P * ASeq) is
  convergent & lim Partial_Sums(P * ASeq) = upper_bound Partial_Sums(P * ASeq)
   & lim
  Partial_Sums(P * ASeq) = P.Union ASeq
proof
  assume ASeq is disjoint_valued;
  then (P * Partial_Union ASeq) = Partial_Sums(P * ASeq) by Th44;
  hence thesis by Th41;
end;
