reserve X for ComplexUnitarySpace;
reserve x, y, w, g, g1, g2 for Point of X;
reserve z for Complex;
reserve p, q, r, M, M1, M2 for Real;
reserve seq, seq1, seq2, seq3 for sequence of X;
reserve k,n,m for Nat;
reserve Nseq for increasing sequence of NAT;

theorem
  seq is constant & (ex n st seq.n = x) implies lim seq = x
proof
  assume that
A1: seq is constant and
A2: ex n st seq.n = x;
  consider n such that
A3: seq.n = x by A2;
  n in NAT by ORDINAL1:def 12;
  then n in dom seq by NORMSP_1:12;
  then x in rng seq by A3,FUNCT_1:def 3;
  hence thesis by A1,Th10;
end;
