reserve rseq, rseq1, rseq2 for Real_Sequence;
reserve seq, seq1, seq2 for Complex_Sequence;
reserve k, n, n1, n2, m for Nat;
reserve p, r for Real;

theorem
  seq1 is convergent & seq2 is convergent & lim(seq1-seq2)=0c implies
  lim seq1 = lim seq2
proof
  assume that
A1: seq1 is convergent & seq2 is convergent and
A2: lim(seq1-seq2)=0c;
  lim(seq1-seq2)=lim(seq1)-lim(seq2) by A1,COMSEQ_2:26;
  hence thesis by A2;
end;
