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 Th4:
  (P * ASeq).n >= 0
proof
A1: n in NAT by ORDINAL1:def 12;
  dom (P * ASeq) = NAT by SEQ_1:1;
  then (P * ASeq).n = P.(ASeq.n) by A1,FUNCT_1:12;
  hence thesis by PROB_1:def 8;
end;
