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;

theorem
  (-x) .|. y = x .|. (-y)
proof
  (-x) .|. y = ((-1)*x) .|. y by RLVECT_1:16
    .= (-1) * x .|. y by Def2
    .= x .|. ((-1)*y) by Def2;
  hence thesis by RLVECT_1:16;
end;
