Inductive Point :=
  P0 | P1 | P2 | P3.Inductive Point :=
  P0 | P1 | P2 | P3.Inductive Point :=
  P0 | P1 | P2 | P3.Inductive Point :=
  P0 | P1 | P2 | P3.Inductive Point :=
  P0 | P1 | P2 | P3.Definition Bet (A B C : Point) :=
  A = B \/ B = C \/ A = C.Definition Cong (A B C D : Point) :=
  (A = B /\ C = D) \/ (A <> B /\ C <> D).

Lemma euclid : forall A B C, ~ (Bet A B C \/ Bet B C A \/ Bet C A B) -> exists CC, Cong A CC B CC /\ Cong A CC C CC.