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 Th1:
  seq is constant implies seq is convergent
proof
  assume seq is constant;
  then consider x such that
A1: for n being Nat holds seq.n = x by VALUED_0:def 18;
  take g = x;
  let r such that
A2: r > 0;
  take m = 0;
  let n such that n >= m;
  dist((seq.n) , g) = dist(x, g) by A1
    .= 0 by CSSPACE:50;
  hence thesis by A2;
end;
