proposition: Lemma nonterminal_to_positive_to_nonterminal nt : positive_to_nonterminal (nonterminal_to_positive nt) = nt.
proof: Proof. unfold nonterminal_to_positive, positive_to_nonterminal. rewrite Nat2Pos.id_max; simpl. reflexivity. Qed.
imports: Coq.PArith.BinPos Coq.PArith.Pnat Coq.Arith.Arith Coq.FSets.FMapInterface Coq.FSets.FMapPositive Fiat.Parsers.ContextFreeGrammar.Carriers Fiat.Common.List.ListFacts Fiat.Common.List.ListMorphisms Fiat.Common.Prod