Section Intuitionistic_Tarski_to_Tarski.
Context `{BTn:intuitionistic_Tarski_neutral_dimensionless}.
Definition BetT A B C := IBet A B C \/ A=B \/ B=C.
(* Lemma 4.1 page 22 *)

Lemma lower_dim :
~ (BetT beeson_s_axioms.PA beeson_s_axioms.PB beeson_s_axioms.PC \/
BetT beeson_s_axioms.PB beeson_s_axioms.PC beeson_s_axioms.PA \/
BetT beeson_s_axioms.PC beeson_s_axioms.PA beeson_s_axioms.PB).