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 Th12:
  x .|. (y - z) = x .|. y - x .|. z
proof
  x .|. (y - z) = x .|. y + x .|. (-z) by Def2
    .= x .|. y + ( - x .|. z ) by Th8;
  hence thesis;
end;
