reserve P for Subset of TOP-REAL 2,
  f,f1,f2,g for FinSequence of TOP-REAL 2,
  p,p1,p2,q,q1,q2 for Point of TOP-REAL 2,
  r1,r2,r19,r29 for Real,
  i,j,k,n for Nat;

theorem Th9:
  for i being Nat holds i+1 <= len(f-:p) implies LSeg(f-:p,i) = LSeg(f,i)
proof
  let i be Nat;
  f-:p = f|(p..f) by FINSEQ_5:def 1;
  hence thesis by Th3;
end;
