fact: Definition up_subst_ren_pure_term_pure_term (sigma : ( nat ) -> pure_term ) (zetapure_term : ( nat ) -> nat ) (theta : ( nat ) -> pure_term ) (Eq : forall x, (funcomp (ren_pure_term zetapure_term) sigma) x = theta x) : forall x, (funcomp (ren_pure_term (upRen_pure_term_pure_term zetapure_term)) (up_pure_term_pure_term sigma)) x = (up_pure_term_pure_term theta) x := fun n => match n with | S n => eq_trans (compRenRen_pure_term shift (upRen_pure_term_pure_term zetapure_term) (funcomp shift zetapure_term) (fun x => eq_refl) (sigma n)) (eq_trans (eq_sym (compRenRen_pure_term zetapure_term shift (funcomp shift zetapure_term) (fun x => eq_refl) (sigma n))) (ap (ren_pure_term shift) (Eq n))) | 0 => eq_refl end.
imports: Undecidability.SystemF.Autosubst.unscoped Undecidability.SystemF.SysF Morphisms