proposition: Lemma pred_lt_beq_helper {valid nt x} : (negb (Nat.eqb x 0) && is_valid_nonterminal valid nt)%bool = true -> pred x < x.
proof: Proof. intro is_valid. generalize (proj1 (proj1 (Bool.andb_true_iff _ _) is_valid)). apply pred_lt_beq. Defined.
imports: Fiat.Common.Coq__8_4__8_5__Compat Coq.Lists.List Coq.ZArith.ZArith Fiat.Parsers.ContextFreeGrammar.Core Fiat.Parsers.BaseTypes Fiat.Parsers.GenericBaseTypes Fiat.Common.Wf