%   ORIGINAL: h4/integerRing/int__ring__thms_c55
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/ring/ring__accessors_c1: !f1 f0 f a0 a. h4/ring/ring__R1 (h4/ring/ring0 a a0 f f0 f1) = a0
% Assm: h4/ring/ring__accessors_c4: !f1 f0 f a0 a. h4/ring/ring__RN (h4/ring/ring0 a a0 f f0 f1) = f1
% Assm: h4/ringNorm/polynom__normalize__def_c0: !r i. h4/ringNorm/polynom__normalize r (h4/ringNorm/Pvar i) = h4/canonical/Cons__varlist (h4/list/CONS i h4/list/NIL) h4/canonical/Nil__monom
% Assm: h4/ringNorm/polynom__normalize__def_c1: !r c. h4/ringNorm/polynom__normalize r (h4/ringNorm/Pconst c) = h4/canonical/Cons__monom c h4/list/NIL h4/canonical/Nil__monom
% Assm: h4/ringNorm/polynom__normalize__def_c2: !r pr pl. h4/ringNorm/polynom__normalize r (h4/ringNorm/Pplus pl pr) = h4/ringNorm/r__canonical__sum__merge r (h4/ringNorm/polynom__normalize r pl) (h4/ringNorm/polynom__normalize r pr)
% Assm: h4/ringNorm/polynom__normalize__def_c3: !r pr pl. h4/ringNorm/polynom__normalize r (h4/ringNorm/Pmult pl pr) = h4/ringNorm/r__canonical__sum__prod r (h4/ringNorm/polynom__normalize r pl) (h4/ringNorm/polynom__normalize r pr)
% Assm: h4/ringNorm/polynom__normalize__def_c4: !r p. h4/ringNorm/polynom__normalize r (h4/ringNorm/Popp p) = h4/ringNorm/r__canonical__sum__scalar3 r (h4/ring/ring__RN r (h4/ring/ring__R1 r)) h4/list/NIL (h4/ringNorm/polynom__normalize r p)
% Assm: h4/integerRing/int__polynom__normalize__def: h4/integerRing/int__polynom__normalize = h4/ringNorm/polynom__normalize (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/integerRing/int__r__canonical__sum__merge__def: h4/integerRing/int__r__canonical__sum__merge = h4/ringNorm/r__canonical__sum__merge (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/integerRing/int__r__canonical__sum__scalar3__def: h4/integerRing/int__r__canonical__sum__scalar3 = h4/ringNorm/r__canonical__sum__scalar3 (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/integerRing/int__r__canonical__sum__prod__def: h4/integerRing/int__r__canonical__sum__prod = h4/ringNorm/r__canonical__sum__prod (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Goal: !p. h4/integerRing/int__polynom__normalize (h4/ringNorm/Popp p) = h4/integerRing/int__r__canonical__sum__scalar3 (h4/integer/int__neg h4/integer/int__1) h4/list/NIL (h4/integerRing/int__polynom__normalize p)
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_rings_ringu_u_accessorsu_c1]: !f1 f0 f a0 a. h4/ring/ring__R1 (h4/ring/ring0 a a0 f f0 f1) = a0
% Assm [h4s_rings_ringu_u_accessorsu_c4]: !f1 f0 f a0 a. h4/ring/ring__RN (h4/ring/ring0 a a0 f f0 f1) = f1
% Assm [h4s_ringNorms_polynomu_u_normalizeu_u_defu_c0]: !r i. happ (h4/ringNorm/polynom__normalize r) (h4/ringNorm/Pvar i) = h4/canonical/Cons__varlist (h4/list/CONS i h4/list/NIL) h4/canonical/Nil__monom
% Assm [h4s_ringNorms_polynomu_u_normalizeu_u_defu_c1]: !r c. happ (h4/ringNorm/polynom__normalize r) (h4/ringNorm/Pconst c) = h4/canonical/Cons__monom c h4/list/NIL h4/canonical/Nil__monom
% Assm [h4s_ringNorms_polynomu_u_normalizeu_u_defu_c2]: !r pr pl. happ (h4/ringNorm/polynom__normalize r) (h4/ringNorm/Pplus pl pr) = happ (happ (h4/ringNorm/r__canonical__sum__merge r) (happ (h4/ringNorm/polynom__normalize r) pl)) (happ (h4/ringNorm/polynom__normalize r) pr)
% Assm [h4s_ringNorms_polynomu_u_normalizeu_u_defu_c3]: !r pr pl. happ (h4/ringNorm/polynom__normalize r) (h4/ringNorm/Pmult pl pr) = happ (happ (h4/ringNorm/r__canonical__sum__prod r) (happ (h4/ringNorm/polynom__normalize r) pl)) (happ (h4/ringNorm/polynom__normalize r) pr)
% Assm [h4s_ringNorms_polynomu_u_normalizeu_u_defu_c4]: !r p. happ (h4/ringNorm/polynom__normalize r) (h4/ringNorm/Popp p) = happ (happ (happ (h4/ringNorm/r__canonical__sum__scalar3 r) (happ (h4/ring/ring__RN r) (h4/ring/ring__R1 r))) h4/list/NIL) (happ (h4/ringNorm/polynom__normalize r) p)
% Assm [h4s_integerRings_intu_u_polynomu_u_normalizeu_u_def]: h4/integerRing/int__polynom__normalize = h4/ringNorm/polynom__normalize (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_mergeu_u_def]: h4/integerRing/int__r__canonical__sum__merge = h4/ringNorm/r__canonical__sum__merge (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_scalar3u_u_def]: h4/integerRing/int__r__canonical__sum__scalar3 = h4/ringNorm/r__canonical__sum__scalar3 (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_produ_u_def]: h4/integerRing/int__r__canonical__sum__prod = h4/ringNorm/r__canonical__sum__prod (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Goal: !p. happ h4/integerRing/int__polynom__normalize (h4/ringNorm/Popp p) = happ (happ (happ h4/integerRing/int__r__canonical__sum__scalar3 (happ h4/integer/int__neg h4/integer/int__1)) h4/list/NIL) (happ h4/integerRing/int__polynom__normalize p)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q167181,TV_Q167177]: ![V_f, V_g]: (![V_x]: s(TV_Q167177,happ(s(t_fun(TV_Q167181,TV_Q167177),V_f),s(TV_Q167181,V_x))) = s(TV_Q167177,happ(s(t_fun(TV_Q167181,TV_Q167177),V_g),s(TV_Q167181,V_x))) => s(t_fun(TV_Q167181,TV_Q167177),V_f) = s(t_fun(TV_Q167181,TV_Q167177),V_g))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_rings_ringu_u_accessorsu_c1, axiom, ![TV_u_27a]: ![V_f1, V_f0, V_f, V_a0, V_a]: s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ring0(s(TV_u_27a,V_a),s(TV_u_27a,V_a0),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f0),s(t_fun(TV_u_27a,TV_u_27a),V_f1))))) = s(TV_u_27a,V_a0)).
fof(ah4s_rings_ringu_u_accessorsu_c4, axiom, ![TV_u_27a]: ![V_f1, V_f0, V_f, V_a0, V_a]: s(t_fun(TV_u_27a,TV_u_27a),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ring0(s(TV_u_27a,V_a),s(TV_u_27a,V_a0),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f0),s(t_fun(TV_u_27a,TV_u_27a),V_f1))))) = s(t_fun(TV_u_27a,TV_u_27a),V_f1)).
fof(ah4s_ringNorms_polynomu_u_normalizeu_u_defu_c0, axiom, ![TV_u_27a]: ![V_r, V_i]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_pvar(s(t_h4s_quotes_index,V_i))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,V_i),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom)))).
fof(ah4s_ringNorms_polynomu_u_normalizeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_r, V_c]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_pconst(s(TV_u_27a,V_c))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_consu_u_monom(s(TV_u_27a,V_c),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom)))).
fof(ah4s_ringNorms_polynomu_u_normalizeu_u_defu_c2, axiom, ![TV_u_27a]: ![V_r, V_pr, V_pl]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_pplus(s(t_h4s_ringNorms_polynom(TV_u_27a),V_pl),s(t_h4s_ringNorms_polynom(TV_u_27a),V_pr))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_pl))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_pr)))))).
fof(ah4s_ringNorms_polynomu_u_normalizeu_u_defu_c3, axiom, ![TV_u_27a]: ![V_r, V_pr, V_pl]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_pmult(s(t_h4s_ringNorms_polynom(TV_u_27a),V_pl),s(t_h4s_ringNorms_polynom(TV_u_27a),V_pr))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_prod(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_pl))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_pr)))))).
fof(ah4s_ringNorms_polynomu_u_normalizeu_u_defu_c4, axiom, ![TV_u_27a]: ![V_r, V_p]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_popp(s(t_h4s_ringNorms_polynom(TV_u_27a),V_p))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar3(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),V_r))))))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_p)))))).
fof(ah4s_integerRings_intu_u_polynomu_u_normalizeu_u_def, axiom, s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_polynomu_u_normalize) = s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_mergeu_u_def, axiom, s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_merge) = s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_scalar3u_u_def, axiom, s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_scalar3) = s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar3(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_produ_u_def, axiom, s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_prod) = s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_prod(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ch4s_integerRings_intu_u_ringu_u_thmsu_c55, conjecture, ![V_p]: s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_polynomu_u_normalize),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),h4s_ringnorms_popp(s(t_h4s_ringNorms_polynom(t_h4s_integers_int),V_p))))) = s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_scalar3),s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg),s(t_h4s_integers_int,h4s_integers_intu_u_1))))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_polynomu_u_normalize),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),V_p)))))).
