for X being non empty TopSpace
for Y, X1, X2 being non empty SubSpace of X st X1 meets X2 holds
( ( X1,Y are_weakly_separated & X2,Y are_weakly_separated implies X1 meet X2,Y are_weakly_separated ) & ( Y,X1 are_weakly_separated & Y,X2 are_weakly_separated implies Y,X1 meet X2 are_weakly_separated ) )