for X being non empty TopSpace
for X0, X1, X2 being non empty SubSpace of X holds
( ( ( X1 misses X0 or X0 misses X1 ) & ( X2 meets X0 or X0 meets X2 ) implies ( (X1 union X2) meet X0 = X2 meet X0 & X0 meet (X1 union X2) = X0 meet X2 ) ) & ( ( X1 meets X0 or X0 meets X1 ) & ( X2 misses X0 or X0 misses X2 ) implies ( (X1 union X2) meet X0 = X1 meet X0 & X0 meet (X1 union X2) = X0 meet X1 ) ) )