proposition: Lemma In_s_rule_spec t a b a' b' : let '(s, phi) := s_rule (a, b, (a', b')) in In t (s::phi) -> In_s_rule t a b a' b'.
proof: Proof. move=> /= [|[|/in_map_iff [?] []]]. all: by eauto using In_s_rule, esym with nocore. Qed.
imports: Undecidability.IntersectionTypes.CD Undecidability.IntersectionTypes.Util.CD_facts Undecidability.StringRewriting.SSTS Undecidability.LambdaCalculus.Util.term_facts Relations List PeanoNat Lia ssreflect ssrfun