Register dec_True as core.dec.True.
Register dec_False as core.dec.False.
Register dec_or as core.dec.or.
Register dec_and as core.dec.and.
Register dec_not as core.dec.not.
Register dec_imp as core.dec.imp.
Register dec_iff as core.dec.iff.
Register dec_not_not as core.dec.not_not.
Register not_not as core.dec.dec_not_not.
Register not_or as core.dec.not_or.
Register not_and as core.dec.not_and.
Register not_imp as core.dec.not_imp.
Register imp_simp as core.dec.imp_simp.
Register not_iff as core.dec.not_iff.
(** Results formulated with iff, used in FSetDecide. Negation are expanded since it is unclear whether setoid rewrite will always perform conversion. *)
(** We begin with lemmas that, when read from left to right, can be understood as ways to eliminate uses of [not]. *)

Theorem not_not_iff : forall A:Prop, decidable A ->
(((A -> False) -> False) <-> A).