%   ORIGINAL: h4/rich__list/EVERY__TAKE
% 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/TRUTH: T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/arithmetic/ADD__0: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/rich__list/TAKE__SEG: !n l. h4/arithmetic/_3C_3D n (h4/list/LENGTH l) ==> h4/list/TAKE n l = h4/rich__list/SEG n h4/num/0 l
% Assm: h4/rich__list/EVERY__SEG: !l P. h4/list/EVERY P l ==> (!m k. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m k) (h4/list/LENGTH l) ==> h4/list/EVERY P (h4/rich__list/SEG m k l))
% Goal: !l P. h4/list/EVERY P l ==> (!m. h4/arithmetic/_3C_3D m (h4/list/LENGTH l) ==> h4/list/EVERY P (h4/list/TAKE m l))
%   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_TRUTH]: T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_arithmetics_ADDu_u_0]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_richu_u_lists_TAKEu_u_SEG]: !n l. h4/arithmetic/_3C_3D n (h4/list/LENGTH l) ==> h4/list/TAKE n l = h4/rich__list/SEG n h4/num/0 l
% Assm [h4s_richu_u_lists_EVERYu_u_SEG]: !l P. h4/list/EVERY P l ==> (!m k. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m k) (h4/list/LENGTH l) ==> h4/list/EVERY P (h4/rich__list/SEG m k l))
% Goal: !l P. h4/list/EVERY P l ==> (!m. h4/arithmetic/_3C_3D m (h4/list/LENGTH l) ==> h4/list/EVERY P (h4/list/TAKE m l))
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_Q162483,TV_Q162479]: ![V_f, V_g]: (![V_x]: s(TV_Q162479,happ(s(t_fun(TV_Q162483,TV_Q162479),V_f),s(TV_Q162483,V_x))) = s(TV_Q162479,happ(s(t_fun(TV_Q162483,TV_Q162479),V_g),s(TV_Q162483,V_x))) => s(t_fun(TV_Q162483,TV_Q162479),V_f) = s(t_fun(TV_Q162483,TV_Q162479),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_arithmetics_ADDu_u_0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_richu_u_lists_TAKEu_u_SEG, axiom, ![TV_u_27a]: ![V_n, V_l]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => s(t_h4s_lists_list(TV_u_27a),h4s_lists_take(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_seg(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(TV_u_27a),V_l))))).
fof(ah4s_richu_u_lists_EVERYu_u_SEG, axiom, ![TV_u_27a]: ![V_l, V_P]: (p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))) => ![V_m, V_k]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_k))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_seg(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_k),s(t_h4s_lists_list(TV_u_27a),V_l))))))))).
fof(ch4s_richu_u_lists_EVERYu_u_TAKE, conjecture, ![TV_u_27a]: ![V_l, V_P]: (p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))) => ![V_m]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_take(s(t_h4s_nums_num,V_m),s(t_h4s_lists_list(TV_u_27a),V_l))))))))).
