%   ORIGINAL: h4/semi__ring/semi__ring__fn__updates_c3
% 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/semi__ring/semi__ring__SRM__fupd0: !f1 f0 f a0 a. h4/semi__ring/semi__ring__SRM__fupd f1 (h4/semi__ring/semi__ring0 a a0 f f0) = h4/semi__ring/semi__ring0 a a0 f (f1 f0)
% Goal: !f1 f0 f a0 a. h4/semi__ring/semi__ring__SRM__fupd f1 (h4/semi__ring/semi__ring0 a a0 f f0) = h4/semi__ring/semi__ring0 a a0 f (f1 f0)
%   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_semiu_u_rings_semiu_u_ringu_u_SRMu_u_fupd0]: !f1 f0 f a0 a. h4/semi__ring/semi__ring__SRM__fupd f1 (h4/semi__ring/semi__ring0 a a0 f f0) = h4/semi__ring/semi__ring0 a a0 f (happ f1 f0)
% Goal: !f1 f0 f a0 a. h4/semi__ring/semi__ring__SRM__fupd f1 (h4/semi__ring/semi__ring0 a a0 f f0) = h4/semi__ring/semi__ring0 a a0 f (happ f1 f0)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f2)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f2))).
fof(aHLu_EXT, axiom, ![TV_Q13427,TV_Q13423]: ![V_f, V_g]: (![V_x]: s(TV_Q13423,happ(s(t_fun(TV_Q13427,TV_Q13423),V_f),s(TV_Q13427,V_x))) = s(TV_Q13423,happ(s(t_fun(TV_Q13427,TV_Q13423),V_g),s(TV_Q13427,V_x))) => s(t_fun(TV_Q13427,TV_Q13423),V_f) = s(t_fun(TV_Q13427,TV_Q13423),V_g))).
fof(ah4s_semiu_u_rings_semiu_u_ringu_u_SRMu_u_fupd0, axiom, ![TV_u_27a]: ![V_f1, V_f0, V_f, V_a0, V_a]: 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_f1),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_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_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_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)),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_f1),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f0)))))).
fof(ch4s_semiu_u_rings_semiu_u_ringu_u_fnu_u_updatesu_c3, conjecture, ![TV_u_27a]: ![V_f1, V_f0, V_f, V_a0, V_a]: 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_f1),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_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_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_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)),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_f1),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f0)))))).
