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
  seq1-(seq2+seq3)=seq1-seq2-seq3
proof
  thus seq1-(seq2+seq3)=seq1+(-1r)(#)(seq2+seq3)
    .=seq1+((-1r)(#)seq2+(-1r)(#)seq3) by Th16
    .=seq1+(-seq2+(-1r)(#)seq3)
    .=seq1+(-seq2+-seq3)
    .=seq1-seq2-seq3 by Th7;
end;
