proposition: Lemma hd_productions_is_reachable (p : production Char) (ps : productions Char) (H : productions_is_reachable (p :: ps)) : production_is_reachable G p.
proof: Proof. destruct H as [nt H]; exists nt. eexists nil; simpl. destruct H as [prefix [? H]]; split; try assumption; []. rewrite <- H; clear. induction prefix as [|x xs IHxs]; simpl. { left; reflexivity. } { right; assumption. } Qed.
imports: Fiat.Common.Coq__8_4__8_5__Compat Coq.Lists.List Coq.Arith.EqNat Coq.Arith.Compare_dec Coq.Arith.Wf_nat Coq.ZArith.ZArith Fiat.Common.List.Operations Fiat.Parsers.ContextFreeGrammar.Core Fiat.Parsers.BaseTypes Fiat.Parsers.GenericBaseTypes Fiat.Parsers.GenericCorrectnessBaseTypes Fiat.Parsers.StringLike.Properties Fiat.Parsers.MinimalParse Fiat.Parsers.CorrectnessBaseTypes Fiat.Parsers.BaseTypesLemmas Fiat.Parsers.ContextFreeGrammar.Properties Fiat.Parsers.WellFoundedParse Fiat.Parsers.MinimalParseOfParse Fiat.Parsers.GenericRecognizer Fiat.Parsers.GenericRecognizerExt Fiat.Common.Wf Fiat.Common.Wf1 Fiat.Common.List.ListFacts Fiat.Common.NatFacts Fiat.Common.UIP Fiat.Common