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 & seq = a * seq1 implies seq is constant
proof
  assume that
A1: seq1 is constant and
A2: seq = a * seq1;
  consider x such that
A3: for n being Nat holds seq1.n = x by A1;
  take z = a * x;
  let n be Nat;
  thus seq.n = a * seq1.n by A2,CLVECT_1:def 14
    .= z by A3;
end;
