%   ORIGINAL: h4/integerRing/int__ring__thms_c42
% 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/ringNorm/interp__vl__def_c0: !vm r. h4/ringNorm/r__interp__vl r vm h4/list/NIL = h4/ring/ring__R1 r
% Assm: h4/ringNorm/interp__vl__def_c1: !x vm t r. h4/ringNorm/r__interp__vl r vm (h4/list/CONS x t) = h4/ringNorm/r__ivl__aux r vm x t
% Assm: h4/integerRing/int__r__ivl__aux__def: h4/integerRing/int__r__ivl__aux = h4/ringNorm/r__ivl__aux (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__interp__vl__def: h4/integerRing/int__r__interp__vl = h4/ringNorm/r__interp__vl (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Goal: !x vm t. h4/integerRing/int__r__interp__vl vm (h4/list/CONS x t) = h4/integerRing/int__r__ivl__aux vm x t
%   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_ringNorms_interpu_u_vlu_u_defu_c0]: !vm r. happ (happ (h4/ringNorm/r__interp__vl r) vm) h4/list/NIL = h4/ring/ring__R1 r
% Assm [h4s_ringNorms_interpu_u_vlu_u_defu_c1]: !x vm t r. happ (happ (h4/ringNorm/r__interp__vl r) vm) (h4/list/CONS x t) = happ (happ (happ (h4/ringNorm/r__ivl__aux r) vm) x) t
% Assm [h4s_integerRings_intu_u_ru_u_ivlu_u_auxu_u_def]: h4/integerRing/int__r__ivl__aux = h4/ringNorm/r__ivl__aux (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_interpu_u_vlu_u_def]: h4/integerRing/int__r__interp__vl = h4/ringNorm/r__interp__vl (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Goal: !x vm t. happ (happ h4/integerRing/int__r__interp__vl vm) (h4/list/CONS x t) = happ (happ (happ h4/integerRing/int__r__ivl__aux vm) x) t
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q166856,TV_Q166852]: ![V_f, V_g]: (![V_x]: s(TV_Q166852,happ(s(t_fun(TV_Q166856,TV_Q166852),V_f),s(TV_Q166856,V_x))) = s(TV_Q166852,happ(s(t_fun(TV_Q166856,TV_Q166852),V_g),s(TV_Q166856,V_x))) => s(t_fun(TV_Q166856,TV_Q166852),V_f) = s(t_fun(TV_Q166856,TV_Q166852),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_ringNorms_interpu_u_vlu_u_defu_c0, axiom, ![TV_u_27a]: ![V_vm, V_r]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),h4s_ringnorms_ru_u_interpu_u_vl(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))) = s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),V_r)))).
fof(ah4s_ringNorms_interpu_u_vlu_u_defu_c1, axiom, ![TV_u_27a]: ![V_x, V_vm, V_t, V_r]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),h4s_ringnorms_ru_u_interpu_u_vl(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,V_x),s(t_h4s_lists_list(t_h4s_quotes_index),V_t))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a))),h4s_ringnorms_ru_u_ivlu_u_aux(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_quotes_index,V_x))),s(t_h4s_lists_list(t_h4s_quotes_index),V_t)))).
fof(ah4s_integerRings_intu_u_ru_u_ivlu_u_auxu_u_def, axiom, s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_ivlu_u_aux) = s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_ringnorms_ru_u_ivlu_u_aux(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_interpu_u_vlu_u_def, axiom, s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),h4s_integerrings_intu_u_ru_u_interpu_u_vl) = s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),h4s_ringnorms_ru_u_interpu_u_vl(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_c42, conjecture, ![V_x, V_vm, V_t]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),h4s_integerrings_intu_u_ru_u_interpu_u_vl),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,V_x),s(t_h4s_lists_list(t_h4s_quotes_index),V_t))))) = s(t_h4s_integers_int,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_ivlu_u_aux),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_quotes_index,V_x))),s(t_h4s_lists_list(t_h4s_quotes_index),V_t)))).
