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 Th18:
  r(#)(seq1-seq2)=r(#)seq1-r(#)seq2
proof
  thus r(#)(seq1-seq2)=r(#)seq1+r(#)(-seq2) by Th16
    .=r(#)seq1+r(#)((-1r)(#)seq2)
    .=r(#)seq1+((-1r)*r)(#)seq2 by Th17
    .=r(#)seq1+(-1r)(#)(r(#)seq2) by Th17
    .=r(#)seq1-(r(#)seq2);
end;
