%   ORIGINAL: h4/integerRing/int__ring__thms_c1
% 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/ringNorm/polynom__simplify__ok: !r. h4/ring/is__ring r ==> (!vm p. h4/ringNorm/r__interp__cs r vm (h4/ringNorm/polynom__simplify r p) = h4/ringNorm/interp__p r vm p)
% Assm: h4/integerRing/int__is__ring: h4/ring/is__ring (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__interp__p__def: h4/integerRing/int__interp__p = h4/ringNorm/interp__p (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__polynom__simplify__def: h4/integerRing/int__polynom__simplify = h4/ringNorm/polynom__simplify (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__cs__def: h4/integerRing/int__r__interp__cs = h4/ringNorm/r__interp__cs (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Goal: !vm p. h4/integerRing/int__interp__p vm p = h4/integerRing/int__r__interp__cs vm (h4/integerRing/int__polynom__simplify 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_ringNorms_polynomu_u_simplifyu_u_ok]: !r. h4/ring/is__ring r ==> (!vm p. happ (happ (h4/ringNorm/r__interp__cs r) vm) (happ (h4/ringNorm/polynom__simplify r) p) = happ (happ (h4/ringNorm/interp__p r) vm) p)
% Assm [h4s_integerRings_intu_u_isu_u_ring]: h4/ring/is__ring (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_interpu_u_pu_u_def]: h4/integerRing/int__interp__p = h4/ringNorm/interp__p (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_polynomu_u_simplifyu_u_def]: h4/integerRing/int__polynom__simplify = h4/ringNorm/polynom__simplify (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_csu_u_def]: h4/integerRing/int__r__interp__cs = h4/ringNorm/r__interp__cs (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Goal: !vm p. happ (happ h4/integerRing/int__interp__p vm) p = happ (happ h4/integerRing/int__r__interp__cs vm) (happ h4/integerRing/int__polynom__simplify 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_Q165823,TV_Q165819]: ![V_f, V_g]: (![V_x]: s(TV_Q165819,happ(s(t_fun(TV_Q165823,TV_Q165819),V_f),s(TV_Q165823,V_x))) = s(TV_Q165819,happ(s(t_fun(TV_Q165823,TV_Q165819),V_g),s(TV_Q165823,V_x))) => s(t_fun(TV_Q165823,TV_Q165819),V_f) = s(t_fun(TV_Q165823,TV_Q165819),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_ringNorms_polynomu_u_simplifyu_u_ok, axiom, ![TV_u_27a]: ![V_r]: (p(s(t_bool,h4s_rings_isu_u_ring(s(t_h4s_rings_ring(TV_u_27a),V_r)))) => ![V_vm, V_p]: s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a)),h4s_ringnorms_ru_u_interpu_u_cs(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),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_simplify(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_p))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_p))))).
fof(ah4s_integerRings_intu_u_isu_u_ring, axiom, p(s(t_bool,h4s_rings_isu_u_ring(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_interpu_u_pu_u_def, axiom, s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p) = s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_ringnorms_interpu_u_p(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_polynomu_u_simplifyu_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_simplify) = 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_simplify(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_csu_u_def, axiom, s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_ru_u_interpu_u_cs) = s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int)),h4s_ringnorms_ru_u_interpu_u_cs(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_c1, conjecture, ![V_vm, V_p]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),V_p))) = s(t_h4s_integers_int,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_ru_u_interpu_u_cs),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),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_simplify),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),V_p)))))).
