proposition: Lemma to_string_length str : List.length (to_string str) = length str.
proof: Proof. induction_to_string str IHlen; trivial. destruct (get 0 str) eqn:H'; simpl; [ rewrite IHlen; reflexivity | ]. apply no_first_char_empty in H'; omega. Qed.
imports: Fiat.Common.Coq__8_4__8_5__Compat Coq.ZArith.ZArith Fiat.Common Fiat.Common.List.Operations Fiat.Common.List.ListFacts Fiat.Common.Le Fiat.Common.Tactics.SetoidSubst Fiat.Common.Tactics.IsClosed Fiat.Parsers.StringLike.Core Fiat.Common.UIP