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
  (seq1/"seq)*Ns = (seq1*Ns)/"(seq*Ns)
proof
  thus (seq1/"seq)*Ns = (seq1(#)(seq"))*Ns .= (seq1*Ns)(#)((seq")*Ns) by Th2
    .= (seq1*Ns)(#)((seq*Ns)") by Th5
    .= (seq1*Ns)/"(seq*Ns);
end;
