proposition: Lemma pure_typing_pure_var_simpleI {Gamma x t} : nth_error Gamma x = Some t -> pure_typing Gamma (pure_var x) t.
proof: Proof. move=> Hx. apply: (pure_typing_pure_var 0); last by apply: rt_refl. rewrite nth_error_map Hx /=. by rewrite ren_poly_type_id. Qed.
imports: List Lia Relation_Definitions Relation_Operators Operators_Properties Undecidability.SystemF.SysF Undecidability.SystemF.Autosubst.syntax Undecidability.SystemF.Autosubst.unscoped Undecidability.SystemF.Util(Facts poly_type_facts pure_term_facts term_facts typing_facts iipc2_facts) ssreflect ssrbool ssrfun