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
  (1 qua Real) * seq = seq
proof
  let n be Element of NAT;
  thus (1 * seq).n = 1 * seq.n by NORMSP_1:def 5
    .= seq.n by RLVECT_1:def 8;
end;
