Theorem ind_HP_Th_termInd : ind_HP_Th P nm v (term_ind P R (build_gterm nm v)) = term_ind P R (sup nm (gtweq_sec nm v)). Proof. use eqweqmap_ap. Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.Induction.PolynomialFunctors. Require Import UniMath.Induction.W.Core. Require Import UniMath.Induction.W.Wtypes. Require Import UniMath.Induction.FunctorAlgebras_legacy. Require Import UniMath.Algebra.Universal.Signatures. Require Import UniMath.Algebra.Universal.Algebras. Require Import UniMath.Algebra.Universal.HVectors. Require Import UniMath.Algebra.Universal.Terms.