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 Th11:
  (x - y) .|. z = x .|. z - y .|. z
proof
  (x - y) .|. z = x .|. z + (-y) .|. z by Def2
    .= x .|. z + ( - y .|. z ) by Th8;
  hence thesis;
end;
