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
  seq = seq + 0.X
proof
  let n be Element of NAT;
  thus (seq + 09(X)).n = seq.n + 09(X) by Def6
    .= seq.n by RLVECT_1:4;
end;
