reserve X for non empty CUNITSTR;
reserve a, b for Complex;
reserve x, y for Point of X;
reserve X for ComplexUnitarySpace;
reserve x, y, z, u, v for Point of X;
reserve seq, seq1, seq2, seq3 for sequence of X;
reserve  n for Nat;

theorem
  seq1 is constant & seq2 is constant & seq = seq1 - seq2 implies
  seq is constant
proof
  assume that
A1: seq1 is constant and
A2: seq2 is constant and
A3: seq = seq1 - seq2;
  consider x such that
A4: for n being Nat holds seq1.n = x by A1;
  consider y such that
A5: for n being Nat holds seq2.n = y by A2;
  take z = x - y;
  let n be Nat;
  thus seq.n = seq1.n - seq2.n by A3,NORMSP_1:def 3
    .= x - seq2.n by A4
    .= z by A5;
end;
