%   ORIGINAL: h4/ring/ring__fn__updates_c0
% 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/ring/ring__R0__fupd0: !f2 f1 f0 f a0 a. h4/ring/ring__R0__fupd f2 (h4/ring/ring0 a a0 f f0 f1) = h4/ring/ring0 (f2 a) a0 f f0 f1
% Goal: !f2 f1 f0 f a0 a. h4/ring/ring__R0__fupd f2 (h4/ring/ring0 a a0 f f0 f1) = h4/ring/ring0 (f2 a) a0 f f0 f1
%   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_rings_ringu_u_R0u_u_fupd0]: !f2 f1 f0 f a0 a. h4/ring/ring__R0__fupd f2 (h4/ring/ring0 a a0 f f0 f1) = h4/ring/ring0 (happ f2 a) a0 f f0 f1
% Goal: !f2 f1 f0 f a0 a. h4/ring/ring__R0__fupd f2 (h4/ring/ring0 a a0 f f0 f1) = h4/ring/ring0 (happ f2 a) a0 f f0 f1
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f3)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f3))).
fof(aHLu_EXT, axiom, ![TV_Q294590,TV_Q294586]: ![V_f, V_g]: (![V_x]: s(TV_Q294586,happ(s(t_fun(TV_Q294590,TV_Q294586),V_f),s(TV_Q294590,V_x))) = s(TV_Q294586,happ(s(t_fun(TV_Q294590,TV_Q294586),V_g),s(TV_Q294590,V_x))) => s(t_fun(TV_Q294590,TV_Q294586),V_f) = s(t_fun(TV_Q294590,TV_Q294586),V_g))).
fof(ah4s_rings_ringu_u_R0u_u_fupd0, axiom, ![TV_u_27a]: ![V_f2, V_f1, V_f0, V_f, V_a0, V_a]: 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_f2),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(t_h4s_rings_ring(TV_u_27a),h4s_rings_ring0(s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_f2),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)))).
fof(ch4s_rings_ringu_u_fnu_u_updatesu_c0, conjecture, ![TV_u_27a]: ![V_f2, V_f1, V_f0, V_f, V_a0, V_a]: 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_f2),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(t_h4s_rings_ring(TV_u_27a),h4s_rings_ring0(s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_f2),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)))).
