proposition: Theorem ind_HP_Hypo_h2map : ind_HP_Hypo P nm v (h2map (λ (s : sorts σ) (t _ : gterm σ s), term_ind P R t) (h1lift v)) = (λ u : B nm, ind lowP e_s (f u)).
proof: Proof. use pathsweq1'. unfold ind_HP_Hypo. rewrite invmap_weqcomp_expand. rewrite inv_helf_weq. rewrite inv_weqonsecfibers. unfold funcomp. rewrite termInd_ind. use h2map_makehvec_basevecfill. Defined.
imports: UniMath.MoreFoundations.All UniMath.Combinatorics.StandardFiniteSets UniMath.Induction.PolynomialFunctors UniMath.Induction.W.Core UniMath.Induction.W.Wtypes UniMath.Induction.FunctorAlgebras_legacy UniMath.Algebra.Universal.Signatures UniMath.Algebra.Universal.Algebras UniMath.Algebra.Universal.HVectors UniMath.Algebra.Universal.Terms