reserve n for Nat;
reserve i for Integer;
reserve r,s,t for Real;
reserve An,Bn,Cn,Dn for Point of TOP-REAL n;
reserve L1,L2 for Element of line_of_REAL n;
reserve A,B,C for Point of TOP-REAL 2;

theorem Th8:
  An <> Cn & An in Line(Bn,Cn) implies Bn in Line(An,Cn)
  proof
    assume that
A1: An <> Cn and
A2: An in Line(Bn,Cn);
    Cn in Line(Bn,Cn) by EUCLID_4:41;
    then Line(Bn,Cn) c= Line(An,Cn) by A1,A2,EUCLID_4:43;
    hence thesis by EUCLID_4:41;
  end;
