theorem Th1:
  for GX being TopSpace, A1,A2,B being Subset of GX
  st A1 is_a_component_of B & A2 is_a_component_of B holds
  A1 = A2 or A1 misses A2
proof
  let GX be TopSpace, A1,A2,B be Subset of GX;
  assume A1 is_a_component_of B;
  then
A1: ex B1 being Subset of GX|B st B1 = A1& B1 is a_component by CONNSP_1:def 6;
  assume A2 is_a_component_of B;
  then ex B2 being Subset of GX|B st B2 = A2 & B2 is a_component
  by CONNSP_1:def 6;
  hence thesis by A1,CONNSP_1:35;
end;
