reserve X for TopSpace;
reserve X for non empty TopSpace;
reserve X1, X2, X3 for non empty SubSpace of X;

theorem Th22:
  X1 is SubSpace of X1 union X2
proof
  set A1 = the carrier of X1, A2 = the carrier of X2, A = the carrier of X1
  union X2;
  A = A1 \/ A2 by Def2;
  then A1 c= A by XBOOLE_1:7;
  hence thesis by Th4;
end;
