
theorem Th21:
  for L being non empty transitive RelStr for x,y being Element of L st x <= y
  holds downarrow x c= downarrow y
proof
  let L be non empty transitive RelStr;
  let x,y be Element of L such that
A1: x <= y;
  let z be object;
  assume
A2: z in downarrow x;
  then reconsider z as Element of L;
  z <= x by A2,Th17;
  then z <= y by A1,ORDERS_2:3;
  hence thesis by Th17;
end;
