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 Th21:
  for S being Segmentation of C, i st 1<=i & i <= len S holds S/.i in C
proof
  let S be Segmentation of C, i;
  assume that
A1: 1<=i and
A2: i <= len S;
  i in dom S by A1,A2,FINSEQ_3:25;
  then
A3: S/.i in rng S by PARTFUN2:2;
  rng S c= C by Def3;
  hence thesis by A3;
end;
