
theorem
  for f being FinSequence of TOP-REAL 2,
  p being Point of TOP-REAL 2 st p in L~f holds
  p in LSeg ( f/.Index(p,f), f/.(Index(p,f)+1) )
proof
  let f be FinSequence of TOP-REAL 2, p be Point of TOP-REAL 2;
  assume
A1: p in L~f;
  then
A2: Index(p,f) < len f by JORDAN3:8;
A3: 1 <= Index(p,f) by A1,JORDAN3:8;
A4: Index(p,f)+1 <= len f by A2,NAT_1:13;
  p in LSeg(f,Index(p,f)) by A1,JORDAN3:9;
  hence thesis by A3,A4,TOPREAL1:def 3;
end;
