reserve r1,r2 for Real;
reserve n,i,i1,i2,j for Nat;
reserve D for non empty set;
reserve f for FinSequence of D;

theorem Th10:
  for f being FinSequence of TOP-REAL 2, p being Point of TOP-REAL
  2 st p in LSeg(f,1) holds Index(p,f) = 1
proof
  let f be FinSequence of TOP-REAL 2, p be Point of TOP-REAL 2;
  assume
A1: p in LSeg(f,1);
  then
A2: Index(p,f) <= 1 by Th7;
  LSeg(f,1) c= L~f by TOPREAL3:19;
  then Index(p,f) >= 1 by A1,Th8;
  hence thesis by A2,XXREAL_0:1;
end;
