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/"seq + seq19/"seq = (seq1+seq19) /" seq & seq1/"seq - seq19/"seq
  = (seq1-seq19) /" seq
proof
  thus seq1/"seq + seq19/"seq = (seq1+seq19)(#)(seq") by Th9
    .= (seq1+seq19) /" seq;
  thus seq1/"seq - seq19/"seq = (seq1-seq19)(#)(seq") by Th14
    .= (seq1-seq19) /" seq;
end;
