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
  (a * b) * seq = a * (b * seq)
proof
  now
    let n be Element of NAT;
    thus ((a * b) * seq).n = (a * b) * seq.n by CLVECT_1:def 14
      .= a * (b * seq.n) by CLVECT_1:def 4
      .= a * (b * seq).n by CLVECT_1:def 14
      .= (a * (b * seq)).n by CLVECT_1:def 14;
  end;
  hence thesis by FUNCT_2:63;
end;
