Require Export GeoCoq.Axioms.tarski_axioms.
Section segment_construction_independent.
Inductive Point :=
P0.
Definition Bet (A B C : Point) := False.
Definition Cong (A B C D : Point) := True.

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.