theorem Th20:
  A,B,C is_a_triangle implies not A in Line(B,C)
  proof
    assume
A1: A,B,C is_a_triangle;
    then
A2: A,B,C are_mutually_distinct by EUCLID_6:20;
    assume A in Line(B,C);
    hence thesis by A1,A2,MENELAUS:13;
  end;
