%   ORIGINAL: h4/lebesgue/max__fn__seq__def__compute_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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/arithmetic/SUC__ELIM__NUMERALS: !g f. (!n. g (h4/num/SUC n) = f n (h4/num/SUC n)) <=> (!n. g (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) = f (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) /\ (!n. g (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) = f (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)))
% Assm: h4/lebesgue/max__fn__seq__def_c0: !x g. h4/lebesgue/max__fn__seq g h4/num/0 x = g h4/num/0 x
% Assm: h4/lebesgue/max__fn__seq__def_c1: !x n g. h4/lebesgue/max__fn__seq g (h4/num/SUC n) x = h4/extreal/extreal__max (h4/lebesgue/max__fn__seq g n x) (g (h4/num/SUC n) x)
% Goal: !x n g. h4/lebesgue/max__fn__seq g (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) x = h4/extreal/extreal__max (h4/lebesgue/max__fn__seq g (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x) (g (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) x)
%   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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_arithmetics_SUCu_u_ELIMu_u_NUMERALS]: !g f. (!n. happ g (h4/num/SUC n) = happ (happ f n) (h4/num/SUC n)) <=> (!n. happ g (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) = happ (happ f (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) /\ (!n. happ g (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) = happ (happ f (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)))
% Assm [h4s_lebesgues_maxu_u_fnu_u_sequ_u_defu_c0]: !x g. h4/lebesgue/max__fn__seq g h4/num/0 x = happ (happ g h4/num/0) x
% Assm [h4s_lebesgues_maxu_u_fnu_u_sequ_u_defu_c1]: !x n g. h4/lebesgue/max__fn__seq g (h4/num/SUC n) x = h4/extreal/extreal__max (h4/lebesgue/max__fn__seq g n x) (happ (happ g (h4/num/SUC n)) x)
% Goal: !x n g. h4/lebesgue/max__fn__seq g (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) x = h4/extreal/extreal__max (h4/lebesgue/max__fn__seq g (h4/arithmetic/_2D (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x) (happ (happ g (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) x)
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_Q269720,TV_Q269716]: ![V_f, V_g]: (![V_x]: s(TV_Q269716,happ(s(t_fun(TV_Q269720,TV_Q269716),V_f),s(TV_Q269720,V_x))) = s(TV_Q269716,happ(s(t_fun(TV_Q269720,TV_Q269716),V_g),s(TV_Q269720,V_x))) => s(t_fun(TV_Q269720,TV_Q269716),V_f) = s(t_fun(TV_Q269720,TV_Q269716),V_g))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_arithmetics_SUCu_u_ELIMu_u_NUMERALS, axiom, ![TV_u_27a]: ![V_g, V_f]: (![V_n]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,TV_u_27a)),V_f),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) <=> (![V_n]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,TV_u_27a)),V_f),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))) & ![V_n]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,TV_u_27a)),V_f),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n)))))))))).
fof(ah4s_lebesgues_maxu_u_fnu_u_sequ_u_defu_c0, axiom, ![TV_u_27a]: ![V_x, V_g]: s(t_h4s_extreals_extreal,h4s_lebesgues_maxu_u_fnu_u_seq(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_extreals_extreal)),V_g),s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,V_x))) = s(t_h4s_extreals_extreal,happ(s(t_fun(TV_u_27a,t_h4s_extreals_extreal),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_extreals_extreal)),V_g),s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_x)))).
fof(ah4s_lebesgues_maxu_u_fnu_u_sequ_u_defu_c1, axiom, ![TV_u_27a]: ![V_x, V_n, V_g]: s(t_h4s_extreals_extreal,h4s_lebesgues_maxu_u_fnu_u_seq(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_extreals_extreal)),V_g),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(TV_u_27a,V_x))) = s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_max(s(t_h4s_extreals_extreal,h4s_lebesgues_maxu_u_fnu_u_seq(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_extreals_extreal)),V_g),s(t_h4s_nums_num,V_n),s(TV_u_27a,V_x))),s(t_h4s_extreals_extreal,happ(s(t_fun(TV_u_27a,t_h4s_extreals_extreal),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_extreals_extreal)),V_g),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))),s(TV_u_27a,V_x)))))).
fof(ch4s_lebesgues_maxu_u_fnu_u_sequ_u_defu_u_computeu_c1, conjecture, ![TV_u_27a]: ![V_x, V_n, V_g]: s(t_h4s_extreals_extreal,h4s_lebesgues_maxu_u_fnu_u_seq(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_extreals_extreal)),V_g),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(TV_u_27a,V_x))) = s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_max(s(t_h4s_extreals_extreal,h4s_lebesgues_maxu_u_fnu_u_seq(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_extreals_extreal)),V_g),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(TV_u_27a,V_x))),s(t_h4s_extreals_extreal,happ(s(t_fun(TV_u_27a,t_h4s_extreals_extreal),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_extreals_extreal)),V_g),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))),s(TV_u_27a,V_x)))))).
