reserve f for Function;
reserve n,k,n1 for Element of NAT;
reserve r,p for Complex;
reserve x,y for set;
reserve seq,seq1,seq2,seq3,seq9,seq19 for Complex_Sequence;

theorem Th14:
  (seq1-seq2)(#)seq3=seq1(#)seq3-seq2(#)seq3
proof
  thus (seq1-seq2)(#)seq3=seq1(#)seq3+(-seq2)(#)seq3 by Th9
    .=seq1(#)seq3+((-1r)(#)seq2)(#)seq3
    .=seq1(#)seq3+(-1r)(#)(seq2(#)seq3) by Th12
    .=seq1(#)seq3-seq2(#)seq3;
end;
