reserve GX for TopSpace;
reserve A, B, C for Subset of GX;
reserve TS for TopStruct;
reserve K, K1, L, L1 for Subset of TS;

theorem
  for GX being non empty TopSpace st for x, y being Point of GX holds x,
  y are_joined holds GX is connected
proof
  let GX be non empty TopSpace;
  assume for x,y being Point of GX holds x,y are_joined;
  then ex x being Point of GX st for y being Point of GX holds x,y are_joined
  by Th29;
  hence thesis by Th28;
end;
