reserve C for Simple_closed_curve,
  p,q,p1 for Point of TOP-REAL 2,
  i,j,k,n for Nat,
  r,s for Real;

theorem Th28:
  for S being Segmentation of C holds Segm(S,len S) /\ Segm(S,1) = {S/.1}
proof
  let S be Segmentation of C;
A1: Segm(S,len S) = Segment(S/.len S,S/.1,C) by Def4;
  len S >= 8 by Def3;
  then 1 < len S by XXREAL_0:2;
  then Segm(S,1) = Segment(S/.1,S/.(1+1),C) by Def4;
  hence thesis by A1,Def3;
end;
