reserve N for Nat;
reserve n,m,n1,n2 for Nat;
reserve q,r,r1,r2 for Real;
reserve x,y for set;
reserve w,w1,w2,g,g1,g2 for Point of TOP-REAL N;
reserve seq,seq1,seq2,seq3,seq9 for Real_Sequence of N;

theorem
  |.r*seq.| = |.r.|(#)|.seq.|
proof
  let n be Element of NAT;
  thus |.r*seq.|.n=|.(r*seq).n.| by Def6
    .=|.r*(seq.n).| by Th5
    .=|.r.|*|.seq.n.| by Th7
    .=|.r.|*(|.seq.|).n by Def6
    .=(|.r.|(#)|.seq.|).n by SEQ_1:9;
end;
