 reserve n for Nat;

theorem THORANGE2:
  for A,B,C,D being Element of TOP-REAL 2 st
    B <> C & B in LSeg(A,C) & C in LSeg(B,D) holds C in LSeg(A,D)
  proof
    let A,B,C,D be Element of TOP-REAL 2;
    assume that
A1: B <> C and
A2: B in LSeg(A,C) and
A3: C in LSeg(B,D);
    reconsider OAS = OASpace(TOP-REAL 2) as OAffinSpace by THQQ;
    reconsider ta = A,tb = B,tc = C,td = D as Element of OAS;
    Mid ta,tb,tc & Mid tb,tc,td by A2,A3,THSS2;
    then ex u,v be Point of TOP-REAL 2 st
      u = ta & v = td & tc in LSeg(u,v) by A1,DIRAF:12,THSS2;
    hence thesis;
  end;
