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;
reserve FSeq for FinSequence of Sigma;

theorem Th60:
  P * FSeq is FinSequence of REAL
proof
  dom (P * FSeq) = dom FSeq by Th59;
  then ex n being Nat st dom (P * FSeq) = Seg n by FINSEQ_1:def 2;
  then reconsider RSeq = P * FSeq as FinSequence by FINSEQ_1:def 2;
  rng (P * FSeq) c= REAL;
  then rng RSeq c= REAL;
  hence thesis by FINSEQ_1:def 4;
end;
