(* * Classical Natural Deduction *)
From Undecidability.FOL Require Export PCPb_to_FOL.
From Undecidability.Synthetic Require Import Definitions DecidabilityFacts EnumerabilityFacts ReducibilityFacts.
(* ** Double Negation Translation *)
Implicit Type b : falsity_flag.
Definition cprv := @prv _ _ falsity_on class.
Instance iUnit (P : Prop) : interp unit.

Lemma cnd_XM:
(forall (phi : form falsity_on), cprv nil phi -> valid phi) ->
forall P, ~~ P -> P.