reserve X for non empty UNITSTR;
reserve a, b for Real;
reserve x, y for Point of X;
reserve X for RealUnitarySpace;
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
  let n be Element of NAT;
  thus ((a * b) * seq).n = (a * b) * seq.n by NORMSP_1:def 5
    .= a * (b * seq.n) by RLVECT_1:def 7
    .= a * (b * seq).n by NORMSP_1:def 5
    .= (a * (b * seq)).n by NORMSP_1:def 5;
end;
