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 Th13:
  p in L~f implies ex i st 1 <= i & i+1 <= len f & p in LSeg(f,i)
proof
  set X = { LSeg(f,i) : 1 <= i & i+1 <= len f};
  assume p in L~f;
  then consider Y being set such that
A1: p in Y and
A2: Y in X by TARSKI:def 4;
  ex i st Y = LSeg(f,i) & 1 <= i & i+1 <= len f by A2;
  hence thesis by A1;
end;
