theorem Th31:
  for S being Segmentation of C holds Segm(S,len S) meets Segm(S,len S -' 1)
proof
  let S be Segmentation of C;
  Segm(S,len S) /\ Segm(S,len S -' 1) = {S/.len S} by Th30;
  hence thesis;
end;
