Definition decidability_of_equality_of_points := forall A B:Tpoint, A=B \/ A<>B.
Definition decidability_of_congruence_of_points := forall A B C D:Tpoint,
Cong A B C D \/ ~ Cong A B C D.
Definition decidability_of_betweenness_of_points := forall A B C:Tpoint,
Bet A B C \/ ~ Bet A B C.

Theorem equivalence_between_decidability_properties_of_basic_relations :
all_equiv  (decidability_of_equality_of_points::
decidability_of_congruence_of_points::
decidability_of_betweenness_of_points::nil).