Section first_order.
Context `{Tn:Tarski_neutral_dimensionless}.
(** Dedekind's axiom of continuity implies the Tarski's axiom schema of continuity *)

Lemma dedekind__fod : dedekind_s_axiom -> first_order_dedekind.
Inductive tFOF :=
eq_fof1 : Tpoint -> Tpoint -> tFOF
| bet_fof1 : Tpoint -> Tpoint -> Tpoint -> tFOF
| cong_fof1 : Tpoint -> Tpoint -> Tpoint -> Tpoint -> tFOF
| not_fof1 : tFOF -> tFOF
| and_fof1 : tFOF -> tFOF -> tFOF
| or_fof1 : tFOF -> tFOF -> tFOF
| implies_fof1 : tFOF -> tFOF -> tFOF
| forall_fof1 : (Tpoint -> tFOF) -> tFOF
| exists_fof1 : (Tpoint -> tFOF) -> tFOF.