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 Th18
    .=seq1+(-seq2-((-1r)(#)seq3))
    .=seq1+(-seq2-(-seq3))
    .=seq1-seq2+seq3 by Th7;
end;
