%   ORIGINAL: h4/llist/LTAKE__EQ__SOME__CONS
% 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/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/EXISTS__REFL: !a. ?x. x = a
% Assm: h4/bool/UNWIND__THM2: !a P. (?x. x = a /\ P x) <=> P a
% Assm: h4/option/option__nchotomy: !opt. opt = h4/option/NONE \/ (?x. opt = h4/option/SOME x)
% Assm: h4/option/option__case__def_c0: !v f. h4/option/option__CASE h4/option/NONE v f = v
% Assm: h4/option/option__case__def_c1: !x v f. h4/option/option__CASE (h4/option/SOME x) v f = f x
% Assm: h4/option/SOME__11: !y x. h4/option/SOME x = h4/option/SOME y <=> x = y
% Assm: h4/option/NOT__NONE__SOME: !x. ~(h4/option/NONE = h4/option/SOME x)
% Assm: h4/option/THE__DEF: !x. h4/option/THE (h4/option/SOME x) = x
% Assm: h4/option/OPTION__MAP__EQ__SOME: !y x f. h4/option/OPTION__MAP f x = h4/option/SOME y <=> (?z. x = h4/option/SOME z /\ y = f z)
% Assm: h4/num/INDUCTION: !P. P h4/num/0 /\ (!n. P n ==> P (h4/num/SUC n)) ==> (!n. P n)
% Assm: h4/llist/llist__CASES: !l. l = h4/llist/LNIL \/ (?h t. l = h4/llist/LCONS h t)
% Assm: h4/llist/LHD__THM_c0: h4/llist/LHD h4/llist/LNIL = h4/option/NONE
% Assm: h4/llist/LHD__THM_c1: !t h. h4/llist/LHD (h4/llist/LCONS h t) = h4/option/SOME h
% Assm: h4/llist/LTL__THM_c0: h4/llist/LTL h4/llist/LNIL = h4/option/NONE
% Assm: h4/llist/LTL__THM_c1: !t h. h4/llist/LTL (h4/llist/LCONS h t) = h4/option/SOME t
% Assm: h4/llist/LTAKE0_c0: !ll. h4/llist/LTAKE h4/num/0 ll = h4/option/SOME h4/list/NIL
% Assm: h4/llist/LTAKE0_c1: !n ll. h4/llist/LTAKE (h4/num/SUC n) ll = h4/option/option__CASE (h4/llist/LHD ll) h4/option/NONE (\hd. h4/option/option__CASE (h4/llist/LTAKE n (h4/option/THE (h4/llist/LTL ll))) h4/option/NONE (\tl. h4/option/SOME (h4/list/CONS hd tl)))
% Assm: h4/llist/LTAKE__THM_c2: !t n h. h4/llist/LTAKE (h4/num/SUC n) (h4/llist/LCONS h t) = h4/option/OPTION__MAP (h4/list/CONS h) (h4/llist/LTAKE n t)
% Goal: !x n l. h4/llist/LTAKE n l = h4/option/SOME x ==> (!h. ?y. h4/llist/LTAKE n (h4/llist/LCONS h l) = h4/option/SOME y)
%   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_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_EXISTSu_u_REFL]: !a. ?x. x = a
% Assm [h4s_bools_UNWINDu_u_THM2]: !a P. (?x. x = a /\ happ P x) <=> happ P a
% Assm [h4s_options_optionu_u_nchotomy]: !opt. opt = h4/option/NONE \/ (?x. opt = h4/option/SOME x)
% Assm [h4s_options_optionu_u_caseu_u_defu_c0]: !v f. h4/option/option__CASE h4/option/NONE v f = v
% Assm [h4s_options_optionu_u_caseu_u_defu_c1]: !x v f. h4/option/option__CASE (h4/option/SOME x) v f = happ f x
% Assm [h4s_options_SOMEu_u_11]: !y x. h4/option/SOME x = h4/option/SOME y <=> x = y
% Assm [h4s_options_NOTu_u_NONEu_u_SOME]: !x. ~(h4/option/NONE = h4/option/SOME x)
% Assm [h4s_options_THEu_u_DEF]: !x. h4/option/THE (h4/option/SOME x) = x
% Assm [h4s_options_OPTIONu_u_MAPu_u_EQu_u_SOME]: !y x f. h4/option/OPTION__MAP f x = h4/option/SOME y <=> (?z. x = h4/option/SOME z /\ y = happ f z)
% Assm [h4s_nums_INDUCTION]: !P. happ P h4/num/0 /\ (!n. happ P n ==> happ P (h4/num/SUC n)) ==> (!n. happ P n)
% Assm [h4s_llists_llistu_u_CASES]: !l. l = h4/llist/LNIL \/ (?h t. l = h4/llist/LCONS h t)
% Assm [h4s_llists_LHDu_u_THMu_c0]: h4/llist/LHD h4/llist/LNIL = h4/option/NONE
% Assm [h4s_llists_LHDu_u_THMu_c1]: !t h. h4/llist/LHD (h4/llist/LCONS h t) = h4/option/SOME h
% Assm [h4s_llists_LTLu_u_THMu_c0]: h4/llist/LTL h4/llist/LNIL = h4/option/NONE
% Assm [h4s_llists_LTLu_u_THMu_c1]: !t h. h4/llist/LTL (h4/llist/LCONS h t) = h4/option/SOME t
% Assm [h4s_llists_LTAKE0u_c0]: !ll. h4/llist/LTAKE h4/num/0 ll = h4/option/SOME h4/list/NIL
% Assm [h4s_llists_LTAKE0u_c1]: !_1. (!hd tl. happ (happ _1 hd) tl = h4/option/SOME (happ (h4/list/CONS hd) tl)) ==> (!_0. (!n ll hd. happ (happ (happ _0 n) ll) hd = h4/option/option__CASE (h4/llist/LTAKE n (h4/option/THE (h4/llist/LTL ll))) h4/option/NONE (happ _1 hd)) ==> (!n ll. h4/llist/LTAKE (h4/num/SUC n) ll = h4/option/option__CASE (h4/llist/LHD ll) h4/option/NONE (happ (happ _0 n) ll)))
% Assm [h4s_llists_LTAKEu_u_THMu_c2]: !t n h. h4/llist/LTAKE (h4/num/SUC n) (h4/llist/LCONS h t) = h4/option/OPTION__MAP (h4/list/CONS h) (h4/llist/LTAKE n t)
% Goal: !x n l. h4/llist/LTAKE n l = h4/option/SOME x ==> (!h. ?y. h4/llist/LTAKE n (h4/llist/LCONS h l) = h4/option/SOME y)
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_Q169774,TV_Q169770]: ![V_f, V_g]: (![V_x]: s(TV_Q169770,happ(s(t_fun(TV_Q169774,TV_Q169770),V_f),s(TV_Q169774,V_x))) = s(TV_Q169770,happ(s(t_fun(TV_Q169774,TV_Q169770),V_g),s(TV_Q169774,V_x))) => s(t_fun(TV_Q169774,TV_Q169770),V_f) = s(t_fun(TV_Q169774,TV_Q169770),V_g))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
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_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
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_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_EXISTSu_u_REFL, axiom, ![TV_u_27a]: ![V_a]: ?[V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_a)).
fof(ah4s_bools_UNWINDu_u_THM2, axiom, ![TV_u_27a]: ![V_a, V_P]: (?[V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_a)))))).
fof(ah4s_options_optionu_u_nchotomy, axiom, ![TV_u_27a]: ![V_opt]: (s(t_h4s_options_option(TV_u_27a),V_opt) = s(t_h4s_options_option(TV_u_27a),h4s_options_none) | ?[V_x]: s(t_h4s_options_option(TV_u_27a),V_opt) = s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))))).
fof(ah4s_options_optionu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27b,h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),h4s_options_none),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(TV_u_27b,V_v)).
fof(ah4s_options_optionu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_v, V_f]: s(TV_u_27b,h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x)))).
fof(ah4s_options_SOMEu_u_11, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))) = s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_y))) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ah4s_options_NOTu_u_NONEu_u_SOME, axiom, ![TV_u_27a]: ![V_x]: ~ (s(t_h4s_options_option(TV_u_27a),h4s_options_none) = s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))))).
fof(ah4s_options_THEu_u_DEF, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_options_the(s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))))) = s(TV_u_27a,V_x)).
fof(ah4s_options_OPTIONu_u_MAPu_u_EQu_u_SOME, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x, V_f]: (s(t_h4s_options_option(TV_u_27b),h4s_options_optionu_u_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_options_option(TV_u_27a),V_x))) = s(t_h4s_options_option(TV_u_27b),h4s_options_some(s(TV_u_27b,V_y))) <=> ?[V_z]: (s(t_h4s_options_option(TV_u_27a),V_x) = s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_z))) & s(TV_u_27b,V_y) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_z)))))).
fof(ah4s_nums_INDUCTION, axiom, ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_0)))) & ![V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))))) => ![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_llists_llistu_u_CASES, axiom, ![TV_u_27a]: ![V_l]: (s(t_h4s_llists_llist(TV_u_27a),V_l) = s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lnil) | ?[V_h, V_t]: s(t_h4s_llists_llist(TV_u_27a),V_l) = s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lcons(s(TV_u_27a,V_h),s(t_h4s_llists_llist(TV_u_27a),V_t))))).
fof(ah4s_llists_LHDu_u_THMu_c0, axiom, ![TV_u_27a]: s(t_h4s_options_option(TV_u_27a),h4s_llists_lhd(s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lnil))) = s(t_h4s_options_option(TV_u_27a),h4s_options_none)).
fof(ah4s_llists_LHDu_u_THMu_c1, axiom, ![TV_u_27b]: ![V_t, V_h]: s(t_h4s_options_option(TV_u_27b),h4s_llists_lhd(s(t_h4s_llists_llist(TV_u_27b),h4s_llists_lcons(s(TV_u_27b,V_h),s(t_h4s_llists_llist(TV_u_27b),V_t))))) = s(t_h4s_options_option(TV_u_27b),h4s_options_some(s(TV_u_27b,V_h)))).
fof(ah4s_llists_LTLu_u_THMu_c0, axiom, ![TV_u_27a]: s(t_h4s_options_option(t_h4s_llists_llist(TV_u_27a)),h4s_llists_ltl(s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lnil))) = s(t_h4s_options_option(t_h4s_llists_llist(TV_u_27a)),h4s_options_none)).
fof(ah4s_llists_LTLu_u_THMu_c1, axiom, ![TV_u_27b]: ![V_t, V_h]: s(t_h4s_options_option(t_h4s_llists_llist(TV_u_27b)),h4s_llists_ltl(s(t_h4s_llists_llist(TV_u_27b),h4s_llists_lcons(s(TV_u_27b,V_h),s(t_h4s_llists_llist(TV_u_27b),V_t))))) = s(t_h4s_options_option(t_h4s_llists_llist(TV_u_27b)),h4s_options_some(s(t_h4s_llists_llist(TV_u_27b),V_t)))).
fof(ah4s_llists_LTAKE0u_c0, axiom, ![TV_u_27a]: ![V_ll]: s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_llists_ltake(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_llists_llist(TV_u_27a),V_ll))) = s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_some(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))).
fof(ah4s_llists_LTAKE0u_c1, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_hd, V_tl]: s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_uu_1),s(TV_u_27a,V_hd))),s(t_h4s_lists_list(TV_u_27a),V_tl))) = s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_some(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_lists_cons(s(TV_u_27a,V_hd))),s(t_h4s_lists_list(TV_u_27a),V_tl))))) => ![V_uu_0]: (![V_n, V_ll, V_hd]: s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(TV_u_27a,t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(TV_u_27a,t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_llists_llist(TV_u_27a),V_ll))),s(TV_u_27a,V_hd))) = s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_optionu_u_case(s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_llists_ltake(s(t_h4s_nums_num,V_n),s(t_h4s_llists_llist(TV_u_27a),h4s_options_the(s(t_h4s_options_option(t_h4s_llists_llist(TV_u_27a)),h4s_llists_ltl(s(t_h4s_llists_llist(TV_u_27a),V_ll))))))),s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_none),s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),V_uu_1),s(TV_u_27a,V_hd))))) => ![V_n, V_ll]: s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_llists_ltake(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_llists_llist(TV_u_27a),V_ll))) = s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),h4s_llists_lhd(s(t_h4s_llists_llist(TV_u_27a),V_ll))),s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_none),s(t_fun(TV_u_27a,t_h4s_options_option(t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(TV_u_27a,t_h4s_options_option(t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(TV_u_27a,t_h4s_options_option(t_h4s_lists_list(TV_u_27a))))),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_llists_llist(TV_u_27a),V_ll)))))))).
fof(ah4s_llists_LTAKEu_u_THMu_c2, axiom, ![TV_u_27c]: ![V_t, V_n, V_h]: s(t_h4s_options_option(t_h4s_lists_list(TV_u_27c)),h4s_llists_ltake(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_llists_llist(TV_u_27c),h4s_llists_lcons(s(TV_u_27c,V_h),s(t_h4s_llists_llist(TV_u_27c),V_t))))) = s(t_h4s_options_option(t_h4s_lists_list(TV_u_27c)),h4s_options_optionu_u_map(s(t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27c)),h4s_lists_cons(s(TV_u_27c,V_h))),s(t_h4s_options_option(t_h4s_lists_list(TV_u_27c)),h4s_llists_ltake(s(t_h4s_nums_num,V_n),s(t_h4s_llists_llist(TV_u_27c),V_t)))))).
fof(ch4s_llists_LTAKEu_u_EQu_u_SOMEu_u_CONS, conjecture, ![TV_u_27a]: ![V_x, V_n, V_l]: (s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_llists_ltake(s(t_h4s_nums_num,V_n),s(t_h4s_llists_llist(TV_u_27a),V_l))) = s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_some(s(t_h4s_lists_list(TV_u_27a),V_x))) => ![V_h]: ?[V_y]: s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_llists_ltake(s(t_h4s_nums_num,V_n),s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lcons(s(TV_u_27a,V_h),s(t_h4s_llists_llist(TV_u_27a),V_l))))) = s(t_h4s_options_option(t_h4s_lists_list(TV_u_27a)),h4s_options_some(s(t_h4s_lists_list(TV_u_27a),V_y))))).
