fact: Definition dedekind_variant := forall (Alpha Beta : Tpoint -> Prop) A C, Alpha A -> Beta C -> (forall P, Out A P C -> Alpha P \/ Beta P) -> (forall X Y, Alpha X -> Beta Y -> Bet A X Y /\ X <> Y) -> (exists B, forall X Y, Alpha X -> Beta Y -> Bet X B Y).
imports: GeoCoq.Tarski_dev.Definitions