theorem Th27:
  for B being Subset of GX, p be Point of GX st p in B holds
  Component_of(p,B)=Component_of Down(p,B)
proof
  let B be Subset of GX, p be Point of GX;
  assume
A1: p in B;
  then p=Down(p,B) by Def3;
  hence thesis by A1,Def7;
end;
