reserve x,X,Y for set;
reserve g,r,r1,r2,p,p1,p2 for Real;
reserve R for Subset of REAL;
reserve seq,seq1,seq2,seq3 for Real_Sequence;
reserve Ns for increasing sequence of NAT;
reserve n for Nat;
reserve W for non empty set;
reserve h,h1,h2 for PartFunc of W,REAL;

theorem
  for h being PartFunc of W,REAL, seq being sequence of W holds
  h is total implies (r(#)h)/*seq = r(#)(h/*seq)
proof
  let h be PartFunc of W,REAL, seq be sequence of W;
  assume h is total;
  then dom h = W by PARTFUN1:def 2;
  then rng seq c= dom h;
  hence thesis by Th9;
end;
