theorem Th23:
  bspace(X) is right_zeroed
proof
  let x be Element of bspace(X);
  reconsider A = x as Subset of X;
  reconsider Z = 0.bspace(X) as Subset of X;
  x+0.bspace(X) = A \+\ Z by Def5
    .= x;
  hence thesis;
end;
