%   ORIGINAL: h4/semi__ring/semi__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/semi__ring/semi__ring__accfupds_c3: !s f. h4/semi__ring/semi__ring__SR1 (h4/semi__ring/semi__ring__SR0__fupd f s) = h4/semi__ring/semi__ring__SR1 s
% Assm: h4/semi__ring/semi__ring__accfupds_c6: !s f. h4/semi__ring/semi__ring__SRP (h4/semi__ring/semi__ring__SR0__fupd f s) = h4/semi__ring/semi__ring__SRP s
% Assm: h4/semi__ring/semi__ring__accfupds_c7: !s f. h4/semi__ring/semi__ring__SRP (h4/semi__ring/semi__ring__SR1__fupd f s) = h4/semi__ring/semi__ring__SRP s
% Assm: h4/semi__ring/semi__ring__accfupds_c9: !s f. h4/semi__ring/semi__ring__SRM (h4/semi__ring/semi__ring__SR0__fupd f s) = h4/semi__ring/semi__ring__SRM s
% Assm: h4/semi__ring/semi__ring__accfupds_c10: !s f. h4/semi__ring/semi__ring__SRM (h4/semi__ring/semi__ring__SR1__fupd f s) = h4/semi__ring/semi__ring__SRM s
% Assm: h4/semi__ring/semi__ring__accfupds_c11: !s f. h4/semi__ring/semi__ring__SRM (h4/semi__ring/semi__ring__SRP__fupd f s) = h4/semi__ring/semi__ring__SRM s
% Assm: h4/semi__ring/semi__ring__accfupds_c12: !s f. h4/semi__ring/semi__ring__SR0 (h4/semi__ring/semi__ring__SR0__fupd f s) = f (h4/semi__ring/semi__ring__SR0 s)
% Assm: h4/semi__ring/semi__ring__accfupds_c13: !s f. h4/semi__ring/semi__ring__SR1 (h4/semi__ring/semi__ring__SR1__fupd f s) = f (h4/semi__ring/semi__ring__SR1 s)
% Assm: h4/semi__ring/semi__ring__accfupds_c14: !s f. h4/semi__ring/semi__ring__SRP (h4/semi__ring/semi__ring__SRP__fupd f s) = f (h4/semi__ring/semi__ring__SRP s)
% Assm: h4/semi__ring/semi__ring__accfupds_c15: !s f. h4/semi__ring/semi__ring__SRM (h4/semi__ring/semi__ring__SRM__fupd f s) = f (h4/semi__ring/semi__ring__SRM s)
% Assm: h4/semi__ring/semi__ring__component__equality: !s2 s1. s1 = s2 <=> h4/semi__ring/semi__ring__SR0 s1 = h4/semi__ring/semi__ring__SR0 s2 /\ h4/semi__ring/semi__ring__SR1 s1 = h4/semi__ring/semi__ring__SR1 s2 /\ h4/semi__ring/semi__ring__SRP s1 = h4/semi__ring/semi__ring__SRP s2 /\ h4/semi__ring/semi__ring__SRM s1 = h4/semi__ring/semi__ring__SRM s2
% Goal: !f2 f1 f02 f01 a2 a1 a02 a01. h4/semi__ring/semi__ring__SR0__fupd (h4/combin/K a01) (h4/semi__ring/semi__ring__SR1__fupd (h4/combin/K a1) (h4/semi__ring/semi__ring__SRP__fupd (h4/combin/K f01) (h4/semi__ring/semi__ring__SRM__fupd (h4/combin/K f1) h4/bool/ARB))) = h4/semi__ring/semi__ring__SR0__fupd (h4/combin/K a02) (h4/semi__ring/semi__ring__SR1__fupd (h4/combin/K a2) (h4/semi__ring/semi__ring__SRP__fupd (h4/combin/K f02) (h4/semi__ring/semi__ring__SRM__fupd (h4/combin/K f2) h4/bool/ARB))) <=> a01 = a02 /\ a1 = a2 /\ 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_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c3]: !s f. h4/semi__ring/semi__ring__SR1 (h4/semi__ring/semi__ring__SR0__fupd f s) = h4/semi__ring/semi__ring__SR1 s
% Assm [h4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c6]: !s f. h4/semi__ring/semi__ring__SRP (h4/semi__ring/semi__ring__SR0__fupd f s) = h4/semi__ring/semi__ring__SRP s
% Assm [h4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c7]: !s f. h4/semi__ring/semi__ring__SRP (h4/semi__ring/semi__ring__SR1__fupd f s) = h4/semi__ring/semi__ring__SRP s
% Assm [h4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c9]: !s f. h4/semi__ring/semi__ring__SRM (h4/semi__ring/semi__ring__SR0__fupd f s) = h4/semi__ring/semi__ring__SRM s
% Assm [h4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c10]: !s f. h4/semi__ring/semi__ring__SRM (h4/semi__ring/semi__ring__SR1__fupd f s) = h4/semi__ring/semi__ring__SRM s
% Assm [h4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c11]: !s f. h4/semi__ring/semi__ring__SRM (h4/semi__ring/semi__ring__SRP__fupd f s) = h4/semi__ring/semi__ring__SRM s
% Assm [h4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c12]: !s f. h4/semi__ring/semi__ring__SR0 (h4/semi__ring/semi__ring__SR0__fupd f s) = happ f (h4/semi__ring/semi__ring__SR0 s)
% Assm [h4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c13]: !s f. h4/semi__ring/semi__ring__SR1 (h4/semi__ring/semi__ring__SR1__fupd f s) = happ f (h4/semi__ring/semi__ring__SR1 s)
% Assm [h4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c14]: !s f. h4/semi__ring/semi__ring__SRP (h4/semi__ring/semi__ring__SRP__fupd f s) = happ f (h4/semi__ring/semi__ring__SRP s)
% Assm [h4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c15]: !s f. h4/semi__ring/semi__ring__SRM (h4/semi__ring/semi__ring__SRM__fupd f s) = happ f (h4/semi__ring/semi__ring__SRM s)
% Assm [h4s_semiu_u_rings_semiu_u_ringu_u_componentu_u_equality]: !s2 s1. s1 = s2 <=> h4/semi__ring/semi__ring__SR0 s1 = h4/semi__ring/semi__ring__SR0 s2 /\ h4/semi__ring/semi__ring__SR1 s1 = h4/semi__ring/semi__ring__SR1 s2 /\ h4/semi__ring/semi__ring__SRP s1 = h4/semi__ring/semi__ring__SRP s2 /\ h4/semi__ring/semi__ring__SRM s1 = h4/semi__ring/semi__ring__SRM s2
% Goal: !f2 f1 f02 f01 a2 a1 a02 a01. h4/semi__ring/semi__ring__SR0__fupd (h4/combin/K a01) (h4/semi__ring/semi__ring__SR1__fupd (h4/combin/K a1) (h4/semi__ring/semi__ring__SRP__fupd (h4/combin/K f01) (h4/semi__ring/semi__ring__SRM__fupd (h4/combin/K f1) h4/bool/ARB))) = h4/semi__ring/semi__ring__SR0__fupd (h4/combin/K a02) (h4/semi__ring/semi__ring__SR1__fupd (h4/combin/K a2) (h4/semi__ring/semi__ring__SRP__fupd (h4/combin/K f02) (h4/semi__ring/semi__ring__SRM__fupd (h4/combin/K f2) h4/bool/ARB))) <=> a01 = a02 /\ a1 = a2 /\ 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_Q14727,TV_Q14723]: ![V_f, V_g]: (![V_x]: s(TV_Q14723,happ(s(t_fun(TV_Q14727,TV_Q14723),V_f),s(TV_Q14727,V_x))) = s(TV_Q14723,happ(s(t_fun(TV_Q14727,TV_Q14723),V_g),s(TV_Q14727,V_x))) => s(t_fun(TV_Q14727,TV_Q14723),V_f) = s(t_fun(TV_Q14727,TV_Q14723),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_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c3, axiom, ![TV_u_27a]: ![V_s, V_f]: s(TV_u_27a,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_sr0u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s))))) = s(TV_u_27a,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s)))).
fof(ah4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c6, axiom, ![TV_u_27a]: ![V_s, V_f]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_sr0u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s)))).
fof(ah4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c7, axiom, ![TV_u_27a]: ![V_s, V_f]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_sr1u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s)))).
fof(ah4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c9, axiom, ![TV_u_27a]: ![V_s, V_f]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_sr0u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s)))).
fof(ah4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c10, axiom, ![TV_u_27a]: ![V_s, V_f]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_sr1u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s)))).
fof(ah4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c11, axiom, ![TV_u_27a]: ![V_s, V_f]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_srpu_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_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s)))).
fof(ah4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c12, axiom, ![TV_u_27a]: ![V_s, V_f]: s(TV_u_27a,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_sr0u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(TV_u_27a,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s)))))).
fof(ah4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c13, axiom, ![TV_u_27a]: ![V_s, V_f]: s(TV_u_27a,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_sr1u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(TV_u_27a,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s)))))).
fof(ah4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c14, axiom, ![TV_u_27a]: ![V_s, V_f]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_srpu_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_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s))))) = 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_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s)))))).
fof(ah4s_semiu_u_rings_semiu_u_ringu_u_accfupdsu_c15, axiom, ![TV_u_27a]: ![V_s, V_f]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_srmu_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_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s))))) = 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_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s)))))).
fof(ah4s_semiu_u_rings_semiu_u_ringu_u_componentu_u_equality, axiom, ![TV_u_27a]: ![V_s2, V_s1]: (s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s1) = s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s2) <=> (s(TV_u_27a,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s1))) = s(TV_u_27a,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s2))) & (s(TV_u_27a,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s1))) = s(TV_u_27a,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s2))) & (s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s1))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s2))) & s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s1))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_s2)))))))).
fof(ch4s_semiu_u_rings_semiu_u_ringu_u_literalu_u_11, conjecture, ![TV_u_27a]: ![V_f2, V_f1, V_f02, V_f01, V_a2, V_a1, V_a02, V_a01]: (s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_sr0u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_k(s(TV_u_27a,V_a01))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_sr1u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_k(s(TV_u_27a,V_a1))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_srpu_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_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_srmu_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_f1))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_bools_arb))))))))) = s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_sr0u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_k(s(TV_u_27a,V_a02))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_sr1u_u_fupd(s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_k(s(TV_u_27a,V_a2))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_srpu_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_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ringu_u_srmu_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_f2))),s(t_h4s_semiu_u_rings_semiu_u_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_f01) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f02) & s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f1) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f2)))))).
