Section CantorVariant.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
Definition Nested_bis (A B:nat -> Tpoint -> Prop) :=
(forall n, exists An Bn, A n An /\ B n Bn) /\
(forall n An An', A n An -> A n An' -> An = An') /\
(forall n Bn Bn', B n Bn -> B n Bn' -> Bn = Bn') /\
forall n An Am Bm Bn,
A n An -> A (S n) Am -> B (S n) Bm -> B n Bn -> Bet An Am Bm /\ Bet Am Bm Bn /\ Am <> Bm.
Definition cantor_variant := forall A B, Nested_bis A B ->
exists X, forall n An Bn, A n An -> B n Bn -> Bet An X Bn.

Lemma cantor__cantor_variant : FunctionalChoice_on nat Tpoint ->
cantor_s_axiom <-> cantor_variant.