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 Th5:
  ASeq.n c= BSeq.n implies (P * ASeq).n <= (P * BSeq).n
proof
A1: n in NAT by ORDINAL1:def 12;
  assume ASeq.n c= BSeq.n;
  then P.(ASeq.n) <= P.(BSeq.n) by PROB_1:34;
  then (P * ASeq).n <= P.(BSeq.n) by A1,FUNCT_2:15;
  hence thesis by A1,FUNCT_2:15;
end;
