%   ORIGINAL: h4/rich__list/EXISTS__DROP
% 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/arithmetic/SUB__ADD: !n m. h4/arithmetic/_3C_3D n m ==> h4/arithmetic/_2B (h4/arithmetic/_2D m n) n = m
% Assm: h4/arithmetic/LESS__EQ__REFL: !m. h4/arithmetic/_3C_3D m m
% Assm: h4/rich__list/DROP__SEG: !n l. h4/arithmetic/_3C_3D n (h4/list/LENGTH l) ==> h4/list/DROP n l = h4/rich__list/SEG (h4/arithmetic/_2D (h4/list/LENGTH l) n) n l
% Assm: h4/rich__list/EXISTS__SEG: !m l k. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m k) (h4/list/LENGTH l) ==> (!P. h4/list/EXISTS P (h4/rich__list/SEG m k l) ==> h4/list/EXISTS P l)
% Goal: !m l. h4/arithmetic/_3C_3D m (h4/list/LENGTH l) ==> (!P. h4/list/EXISTS P (h4/list/DROP m l) ==> h4/list/EXISTS P 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_arithmetics_SUBu_u_ADD]: !n m. h4/arithmetic/_3C_3D n m ==> h4/arithmetic/_2B (h4/arithmetic/_2D m n) n = m
% Assm [h4s_arithmetics_LESSu_u_EQu_u_REFL]: !m. h4/arithmetic/_3C_3D m m
% Assm [h4s_richu_u_lists_DROPu_u_SEG]: !n l. h4/arithmetic/_3C_3D n (h4/list/LENGTH l) ==> h4/list/DROP n l = h4/rich__list/SEG (h4/arithmetic/_2D (h4/list/LENGTH l) n) n l
% Assm [h4s_richu_u_lists_EXISTSu_u_SEG]: !m l k. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m k) (h4/list/LENGTH l) ==> (!P. h4/list/EXISTS P (h4/rich__list/SEG m k l) ==> h4/list/EXISTS P l)
% Goal: !m l. h4/arithmetic/_3C_3D m (h4/list/LENGTH l) ==> (!P. h4/list/EXISTS P (h4/list/DROP m l) ==> h4/list/EXISTS P 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_Q162583,TV_Q162579]: ![V_f, V_g]: (![V_x]: s(TV_Q162579,happ(s(t_fun(TV_Q162583,TV_Q162579),V_f),s(TV_Q162583,V_x))) = s(TV_Q162579,happ(s(t_fun(TV_Q162583,TV_Q162579),V_g),s(TV_Q162583,V_x))) => s(t_fun(TV_Q162583,TV_Q162579),V_f) = s(t_fun(TV_Q162583,TV_Q162579),V_g))).
fof(ah4s_arithmetics_SUBu_u_ADD, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))) => s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,V_m))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_REFL, axiom, ![V_m]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_m))))).
fof(ah4s_richu_u_lists_DROPu_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_drop(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,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_l))))).
fof(ah4s_richu_u_lists_EXISTSu_u_SEG, axiom, ![TV_u_27a]: ![V_m, V_l, 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)))))) => ![V_P]: (p(s(t_bool,h4s_lists_exists(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)))))) => p(s(t_bool,h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l))))))).
fof(ch4s_richu_u_lists_EXISTSu_u_DROP, conjecture, ![TV_u_27a]: ![V_m, V_l]: (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)))))) => ![V_P]: (p(s(t_bool,h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_drop(s(t_h4s_nums_num,V_m),s(t_h4s_lists_list(TV_u_27a),V_l)))))) => p(s(t_bool,h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l))))))).
