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 Th27:
  for S being Segmentation of C
  for i,j st 1<=i & i< j & j<len S & i,j are_adjacent
  holds Segm(S,i) meets Segm(S,j)
proof
  let S be Segmentation of C;
  let i,j;
  assume that
A1: 1<=i and
A2: i< j and
A3: j<len S and
A4: i,j are_adjacent;
  Segm(S,i) /\ Segm(S,j)={S/.(i+1)} by A1,A2,A3,A4,Th26;
  hence thesis;
end;
