%   ORIGINAL: h4/ring/ring__literal__11
% 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/combin/K__THM: !y x. h4/combin/K x y = x
% Assm: h4/ring/ring__accfupds_c4: !r f. h4/ring/ring__R1 (h4/ring/ring__R0__fupd f r) = h4/ring/ring__R1 r
% Assm: h4/ring/ring__accfupds_c8: !r f. h4/ring/ring__RP (h4/ring/ring__R0__fupd f r) = h4/ring/ring__RP r
% Assm: h4/ring/ring__accfupds_c9: !r f. h4/ring/ring__RP (h4/ring/ring__R1__fupd f r) = h4/ring/ring__RP r
% Assm: h4/ring/ring__accfupds_c12: !r f. h4/ring/ring__RM (h4/ring/ring__R0__fupd f r) = h4/ring/ring__RM r
% Assm: h4/ring/ring__accfupds_c13: !r f. h4/ring/ring__RM (h4/ring/ring__R1__fupd f r) = h4/ring/ring__RM r
% Assm: h4/ring/ring__accfupds_c14: !r f. h4/ring/ring__RM (h4/ring/ring__RP__fupd f r) = h4/ring/ring__RM r
% Assm: h4/ring/ring__accfupds_c16: !r f. h4/ring/ring__RN (h4/ring/ring__R0__fupd f r) = h4/ring/ring__RN r
% Assm: h4/ring/ring__accfupds_c17: !r f. h4/ring/ring__RN (h4/ring/ring__R1__fupd f r) = h4/ring/ring__RN r
% Assm: h4/ring/ring__accfupds_c18: !r f. h4/ring/ring__RN (h4/ring/ring__RP__fupd f r) = h4/ring/ring__RN r
% Assm: h4/ring/ring__accfupds_c19: !r f. h4/ring/ring__RN (h4/ring/ring__RM__fupd f r) = h4/ring/ring__RN r
% Assm: h4/ring/ring__accfupds_c20: !r f. h4/ring/ring__R0 (h4/ring/ring__R0__fupd f r) = f (h4/ring/ring__R0 r)
% Assm: h4/ring/ring__accfupds_c21: !r f. h4/ring/ring__R1 (h4/ring/ring__R1__fupd f r) = f (h4/ring/ring__R1 r)
% Assm: h4/ring/ring__accfupds_c22: !r f. h4/ring/ring__RP (h4/ring/ring__RP__fupd f r) = f (h4/ring/ring__RP r)
% Assm: h4/ring/ring__accfupds_c23: !r f. h4/ring/ring__RM (h4/ring/ring__RM__fupd f r) = f (h4/ring/ring__RM r)
% Assm: h4/ring/ring__accfupds_c24: !r f. h4/ring/ring__RN (h4/ring/ring__RN__fupd f r) = f (h4/ring/ring__RN r)
% Assm: h4/ring/ring__component__equality: !r2 r1. r1 = r2 <=> h4/ring/ring__R0 r1 = h4/ring/ring__R0 r2 /\ h4/ring/ring__R1 r1 = h4/ring/ring__R1 r2 /\ h4/ring/ring__RP r1 = h4/ring/ring__RP r2 /\ h4/ring/ring__RM r1 = h4/ring/ring__RM r2 /\ h4/ring/ring__RN r1 = h4/ring/ring__RN r2
% Goal: !f2 f12 f11 f1 f02 f01 a2 a1 a02 a01. h4/ring/ring__R0__fupd (h4/combin/K a01) (h4/ring/ring__R1__fupd (h4/combin/K a1) (h4/ring/ring__RP__fupd (h4/combin/K f11) (h4/ring/ring__RM__fupd (h4/combin/K f01) (h4/ring/ring__RN__fupd (h4/combin/K f1) h4/bool/ARB)))) = h4/ring/ring__R0__fupd (h4/combin/K a02) (h4/ring/ring__R1__fupd (h4/combin/K a2) (h4/ring/ring__RP__fupd (h4/combin/K f12) (h4/ring/ring__RM__fupd (h4/combin/K f02) (h4/ring/ring__RN__fupd (h4/combin/K f2) h4/bool/ARB)))) <=> a01 = a02 /\ a1 = a2 /\ f11 = f12 /\ f01 = f02 /\ f1 = f2
%   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_combins_Ku_u_THM]: !y x. happ (h4/combin/K x) y = x
% Assm [h4s_rings_ringu_u_accfupdsu_c4]: !r f. h4/ring/ring__R1 (h4/ring/ring__R0__fupd f r) = h4/ring/ring__R1 r
% Assm [h4s_rings_ringu_u_accfupdsu_c8]: !r f. h4/ring/ring__RP (h4/ring/ring__R0__fupd f r) = h4/ring/ring__RP r
% Assm [h4s_rings_ringu_u_accfupdsu_c9]: !r f. h4/ring/ring__RP (h4/ring/ring__R1__fupd f r) = h4/ring/ring__RP r
% Assm [h4s_rings_ringu_u_accfupdsu_c12]: !r f. h4/ring/ring__RM (h4/ring/ring__R0__fupd f r) = h4/ring/ring__RM r
% Assm [h4s_rings_ringu_u_accfupdsu_c13]: !r f. h4/ring/ring__RM (h4/ring/ring__R1__fupd f r) = h4/ring/ring__RM r
% Assm [h4s_rings_ringu_u_accfupdsu_c14]: !r f. h4/ring/ring__RM (h4/ring/ring__RP__fupd f r) = h4/ring/ring__RM r
% Assm [h4s_rings_ringu_u_accfupdsu_c16]: !r f. h4/ring/ring__RN (h4/ring/ring__R0__fupd f r) = h4/ring/ring__RN r
% Assm [h4s_rings_ringu_u_accfupdsu_c17]: !r f. h4/ring/ring__RN (h4/ring/ring__R1__fupd f r) = h4/ring/ring__RN r
% Assm [h4s_rings_ringu_u_accfupdsu_c18]: !r f. h4/ring/ring__RN (h4/ring/ring__RP__fupd f r) = h4/ring/ring__RN r
% Assm [h4s_rings_ringu_u_accfupdsu_c19]: !r f. h4/ring/ring__RN (h4/ring/ring__RM__fupd f r) = h4/ring/ring__RN r
% Assm [h4s_rings_ringu_u_accfupdsu_c20]: !r f. h4/ring/ring__R0 (h4/ring/ring__R0__fupd f r) = happ f (h4/ring/ring__R0 r)
% Assm [h4s_rings_ringu_u_accfupdsu_c21]: !r f. h4/ring/ring__R1 (h4/ring/ring__R1__fupd f r) = happ f (h4/ring/ring__R1 r)
% Assm [h4s_rings_ringu_u_accfupdsu_c22]: !r f. h4/ring/ring__RP (h4/ring/ring__RP__fupd f r) = happ f (h4/ring/ring__RP r)
% Assm [h4s_rings_ringu_u_accfupdsu_c23]: !r f. h4/ring/ring__RM (h4/ring/ring__RM__fupd f r) = happ f (h4/ring/ring__RM r)
% Assm [h4s_rings_ringu_u_accfupdsu_c24]: !r f. h4/ring/ring__RN (h4/ring/ring__RN__fupd f r) = happ f (h4/ring/ring__RN r)
% Assm [h4s_rings_ringu_u_componentu_u_equality]: !r2 r1. r1 = r2 <=> h4/ring/ring__R0 r1 = h4/ring/ring__R0 r2 /\ h4/ring/ring__R1 r1 = h4/ring/ring__R1 r2 /\ h4/ring/ring__RP r1 = h4/ring/ring__RP r2 /\ h4/ring/ring__RM r1 = h4/ring/ring__RM r2 /\ h4/ring/ring__RN r1 = h4/ring/ring__RN r2
% Goal: !f2 f12 f11 f1 f02 f01 a2 a1 a02 a01. h4/ring/ring__R0__fupd (h4/combin/K a01) (h4/ring/ring__R1__fupd (h4/combin/K a1) (h4/ring/ring__RP__fupd (h4/combin/K f11) (h4/ring/ring__RM__fupd (h4/combin/K f01) (h4/ring/ring__RN__fupd (h4/combin/K f1) h4/bool/ARB)))) = h4/ring/ring__R0__fupd (h4/combin/K a02) (h4/ring/ring__R1__fupd (h4/combin/K a2) (h4/ring/ring__RP__fupd (h4/combin/K f12) (h4/ring/ring__RM__fupd (h4/combin/K f02) (h4/ring/ring__RN__fupd (h4/combin/K f2) h4/bool/ARB)))) <=> a01 = a02 /\ a1 = a2 /\ f11 = f12 /\ f01 = f02 /\ f1 = f2
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_Q296590,TV_Q296586]: ![V_f, V_g]: (![V_x]: s(TV_Q296586,happ(s(t_fun(TV_Q296590,TV_Q296586),V_f),s(TV_Q296590,V_x))) = s(TV_Q296586,happ(s(t_fun(TV_Q296590,TV_Q296586),V_g),s(TV_Q296590,V_x))) => s(t_fun(TV_Q296590,TV_Q296586),V_f) = s(t_fun(TV_Q296590,TV_Q296586),V_g))).
fof(ah4s_combins_Ku_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),h4s_combins_k(s(TV_u_27a,V_x))),s(TV_u_27b,V_y))) = s(TV_u_27a,V_x)).
fof(ah4s_rings_ringu_u_accfupdsu_c4, axiom, ![TV_u_27a]: ![V_r, V_f]: s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),V_f),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)))).
fof(ah4s_rings_ringu_u_accfupdsu_c8, axiom, ![TV_u_27a]: ![V_r, V_f]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_rings_ring(TV_u_27a),V_r))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),V_r)))).
fof(ah4s_rings_ringu_u_accfupdsu_c9, axiom, ![TV_u_27a]: ![V_r, V_f]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_r1u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_rings_ring(TV_u_27a),V_r))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),V_r)))).
fof(ah4s_rings_ringu_u_accfupdsu_c12, axiom, ![TV_u_27a]: ![V_r, V_f]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_rings_ring(TV_u_27a),V_r))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),V_r)))).
fof(ah4s_rings_ringu_u_accfupdsu_c13, axiom, ![TV_u_27a]: ![V_r, V_f]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_r1u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_rings_ring(TV_u_27a),V_r))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),V_r)))).
fof(ah4s_rings_ringu_u_accfupdsu_c14, axiom, ![TV_u_27a]: ![V_r, V_f]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_rpu_u_fupd(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a))),V_f),s(t_h4s_rings_ring(TV_u_27a),V_r))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),V_r)))).
fof(ah4s_rings_ringu_u_accfupdsu_c16, axiom, ![TV_u_27a]: ![V_r, V_f]: s(t_fun(TV_u_27a,TV_u_27a),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_rings_ring(TV_u_27a),V_r))))) = s(t_fun(TV_u_27a,TV_u_27a),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(TV_u_27a),V_r)))).
fof(ah4s_rings_ringu_u_accfupdsu_c17, axiom, ![TV_u_27a]: ![V_r, V_f]: s(t_fun(TV_u_27a,TV_u_27a),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_r1u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_rings_ring(TV_u_27a),V_r))))) = s(t_fun(TV_u_27a,TV_u_27a),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(TV_u_27a),V_r)))).
fof(ah4s_rings_ringu_u_accfupdsu_c18, axiom, ![TV_u_27a]: ![V_r, V_f]: s(t_fun(TV_u_27a,TV_u_27a),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_rpu_u_fupd(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a))),V_f),s(t_h4s_rings_ring(TV_u_27a),V_r))))) = s(t_fun(TV_u_27a,TV_u_27a),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(TV_u_27a),V_r)))).
fof(ah4s_rings_ringu_u_accfupdsu_c19, axiom, ![TV_u_27a]: ![V_r, V_f]: s(t_fun(TV_u_27a,TV_u_27a),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_rmu_u_fupd(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a))),V_f),s(t_h4s_rings_ring(TV_u_27a),V_r))))) = s(t_fun(TV_u_27a,TV_u_27a),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(TV_u_27a),V_r)))).
fof(ah4s_rings_ringu_u_accfupdsu_c20, axiom, ![TV_u_27a]: ![V_r, V_f]: s(TV_u_27a,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_rings_ring(TV_u_27a),V_r))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(TV_u_27a,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(TV_u_27a),V_r)))))).
fof(ah4s_rings_ringu_u_accfupdsu_c21, axiom, ![TV_u_27a]: ![V_r, V_f]: s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_r1u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_rings_ring(TV_u_27a),V_r))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),V_r)))))).
fof(ah4s_rings_ringu_u_accfupdsu_c22, axiom, ![TV_u_27a]: ![V_r, V_f]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_rpu_u_fupd(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a))),V_f),s(t_h4s_rings_ring(TV_u_27a),V_r))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),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)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),V_r)))))).
fof(ah4s_rings_ringu_u_accfupdsu_c23, axiom, ![TV_u_27a]: ![V_r, V_f]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_rmu_u_fupd(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a))),V_f),s(t_h4s_rings_ring(TV_u_27a),V_r))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),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)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),V_r)))))).
fof(ah4s_rings_ringu_u_accfupdsu_c24, axiom, ![TV_u_27a]: ![V_r, V_f]: s(t_fun(TV_u_27a,TV_u_27a),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_rnu_u_fupd(s(t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a)),V_f),s(t_h4s_rings_ring(TV_u_27a),V_r))))) = s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a)),V_f),s(t_fun(TV_u_27a,TV_u_27a),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(TV_u_27a),V_r)))))).
fof(ah4s_rings_ringu_u_componentu_u_equality, axiom, ![TV_u_27a]: ![V_r2, V_r1]: (s(t_h4s_rings_ring(TV_u_27a),V_r1) = s(t_h4s_rings_ring(TV_u_27a),V_r2) <=> (s(TV_u_27a,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(TV_u_27a),V_r1))) = s(TV_u_27a,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(TV_u_27a),V_r2))) & (s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),V_r1))) = s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),V_r2))) & (s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),V_r1))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),V_r2))) & (s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),V_r1))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),V_r2))) & s(t_fun(TV_u_27a,TV_u_27a),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(TV_u_27a),V_r1))) = s(t_fun(TV_u_27a,TV_u_27a),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(TV_u_27a),V_r2))))))))).
fof(ch4s_rings_ringu_u_literalu_u_11, conjecture, ![TV_u_27a]: ![V_f2, V_f12, V_f11, V_f1, V_f02, V_f01, V_a2, V_a1, V_a02, V_a01]: (s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_k(s(TV_u_27a,V_a01))),s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_r1u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_k(s(TV_u_27a,V_a1))),s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_rpu_u_fupd(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a))),h4s_combins_k(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f11))),s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_rmu_u_fupd(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a))),h4s_combins_k(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f01))),s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_rnu_u_fupd(s(t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a)),h4s_combins_k(s(t_fun(TV_u_27a,TV_u_27a),V_f1))),s(t_h4s_rings_ring(TV_u_27a),h4s_bools_arb))))))))))) = s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_r0u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_k(s(TV_u_27a,V_a02))),s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_r1u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_k(s(TV_u_27a,V_a2))),s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_rpu_u_fupd(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a))),h4s_combins_k(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f12))),s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_rmu_u_fupd(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a))),h4s_combins_k(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f02))),s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ringu_u_rnu_u_fupd(s(t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a)),h4s_combins_k(s(t_fun(TV_u_27a,TV_u_27a),V_f2))),s(t_h4s_rings_ring(TV_u_27a),h4s_bools_arb))))))))))) <=> (s(TV_u_27a,V_a01) = s(TV_u_27a,V_a02) & (s(TV_u_27a,V_a1) = s(TV_u_27a,V_a2) & (s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f11) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f12) & (s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f01) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f02) & s(t_fun(TV_u_27a,TV_u_27a),V_f1) = s(t_fun(TV_u_27a,TV_u_27a),V_f2))))))).
