fact: Fixpoint compRenSubst_term (xipoly_type : ( nat ) -> nat ) (xiterm : ( nat ) -> nat ) (taupoly_type : ( nat ) -> poly_type ) (tauterm : ( nat ) -> term ) (thetapoly_type : ( nat ) -> poly_type ) (thetaterm : ( nat ) -> term ) (Eqpoly_type : forall x, (funcomp taupoly_type xipoly_type) x = thetapoly_type x) (Eqterm : forall x, (funcomp tauterm xiterm) x = thetaterm x) (s : term ) : subst_term taupoly_type tauterm (ren_term xipoly_type xiterm s) = subst_term thetapoly_type thetaterm s := match s return subst_term taupoly_type tauterm (ren_term xipoly_type xiterm s) = subst_term thetapoly_type thetaterm s with | var s => Eqterm s | app s0 s1 => congr_app (compRenSubst_term xipoly_type xiterm taupoly_type tauterm thetapoly_type thetaterm Eqpoly_type Eqterm s0) (compRenSubst_term xipoly_type xiterm taupoly_type tauterm thetapoly_type thetaterm Eqpoly_type Eqterm s1) | abs s0 s1 => congr_abs (compRenSubst_poly_type xipoly_type taupoly_type thetapoly_type Eqpoly_type s0) (compRenSubst_term (upRen_term_poly_type xipoly_type) (upRen_term_term xiterm) (up_term_poly_type taupoly_type) (up_term_term tauterm) (up_term_poly_type thetapoly_type) (up_term_term thetaterm) (up_ren_subst_term_poly_type (_) (_) (_) Eqpoly_type) (up_ren_subst_term_term (_) (_) (_) Eqterm) s1) | ty_app s0 s1 => congr_ty_app (compRenSubst_term xipoly_type xiterm taupoly_type tauterm thetapoly_type thetaterm Eqpoly_type Eqterm s0) (compRenSubst_poly_type xipoly_type taupoly_type thetapoly_type Eqpoly_type s1) | ty_abs s0 => congr_ty_abs (compRenSubst_term (upRen_poly_type_poly_type xipoly_type) (upRen_poly_type_term xiterm) (up_poly_type_poly_type taupoly_type) (up_poly_type_term tauterm) (up_poly_type_poly_type thetapoly_type) (up_poly_type_term thetaterm) (up_ren_subst_poly_type_poly_type (_) (_) (_) Eqpoly_type) (up_ren_subst_poly_type_term (_) (_) (_) Eqterm) s0) end.
imports: Undecidability.SystemF.Autosubst.unscoped Undecidability.SystemF.SysF Morphisms