for X being non empty TopSpace
for X1, X2, Y1, Y2 being non empty SubSpace of X st X1 is not SubSpace of X2 & X2 is not SubSpace of X1 & X1 union X2 is SubSpace of Y1 union Y2 & Y1 meet (X1 union X2) is SubSpace of X1 & Y2 meet (X1 union X2) is SubSpace of X2 holds
( Y1 meets X1 union X2 & Y2 meets X1 union X2 )