reserve f for Function;
reserve n,k,n1 for Nat;
reserve r,p for Real;
reserve x,y,z for object;
reserve seq,seq1,seq2,seq3,seq9,seq19 for Real_Sequence;

theorem Th20:
  (seq1 - seq2) (#) seq3 = seq1 (#) seq3 - seq2 (#) seq3
proof
  thus (seq1-seq2)(#)seq3=seq1(#)seq3+(-seq2)(#)seq3 by Th15
    .=seq1(#)seq3-seq2(#)seq3 by Th18;
end;
