reserve X for non empty 1-sorted;
reserve A, A1, A2, B1, B2 for Subset of X;
reserve X for non empty TopSpace;
reserve A, A1, A2, B1, B2 for Subset of X;
reserve X for non empty 1-sorted;
reserve A, A1, A2, B1, B2 for Subset of X;
reserve X for non empty TopSpace,
  A1, A2 for Subset of X;
reserve X0 for non empty SubSpace of X,
  B1, B2 for Subset of X0;
reserve X0, X1, X2, Y1, Y2 for non empty SubSpace of X;
reserve X for non empty TopSpace;

theorem
  for X1, X2, Y1, Y2 being non empty SubSpace of X st X1,Y1
  constitute_a_decomposition & X2,Y2 constitute_a_decomposition holds X1,X2
  are_separated implies Y1,Y2 are_weakly_separated
by TSEP_1:78,Th37;
