
theorem Th6:
  for T being non empty TopSpace, A being non empty Subset of T, B1
,B2,S being Subset of T st B1 is_a_component_of A & B2 is_a_component_of A & S
  is_a_component_of A & B1 \/ B2 = A holds S = B1 or S = B2
proof
  let T be non empty TopSpace, A be non empty Subset of T, B1,B2,S be Subset
  of T such that
A1: B1 is_a_component_of A and
A2: B2 is_a_component_of A and
A3: S is_a_component_of A and
A4: B1 \/ B2 = A;
  S c= A by A3,Th5;
  then S meets A by A3,Th4,XBOOLE_1:67;
  then S meets B1 or S meets B2 by A4,XBOOLE_1:70;
  hence thesis by A1,A2,A3,GOBOARD9:1;
end;
