%   ORIGINAL: h4/container/CARD__LIST__TO__BAG
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/arithmetic/ADD1: !m. h4/num/SUC m = h4/arithmetic/_2B m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/arithmetic/EQ__MONO__ADD__EQ: !p n m. h4/arithmetic/_2B m p = h4/arithmetic/_2B n p <=> m = n
% Assm: h4/list/LENGTH0_c0: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm: h4/list/LENGTH0_c1: !t h. h4/list/LENGTH (h4/list/CONS h t) = h4/num/SUC (h4/list/LENGTH t)
% Assm: h4/list/list__induction: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/bag/BAG__CARD__THM_c0: h4/bag/BAG__CARD h4/bag/EMPTY__BAG = h4/num/0
% Assm: h4/bag/BAG__CARD__THM_c1: !b. h4/bag/FINITE__BAG b ==> (!e. h4/bag/BAG__CARD (h4/bag/BAG__INSERT e b) = h4/arithmetic/_2B (h4/bag/BAG__CARD b) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/container/LIST__TO__BAG__def_c0: h4/container/LIST__TO__BAG h4/list/NIL = h4/bag/EMPTY__BAG
% Assm: h4/container/LIST__TO__BAG__def_c1: !t h. h4/container/LIST__TO__BAG (h4/list/CONS h t) = h4/bag/BAG__INSERT h (h4/container/LIST__TO__BAG t)
% Assm: h4/container/FINITE__LIST__TO__BAG: !ls. h4/bag/FINITE__BAG (h4/container/LIST__TO__BAG ls)
% Goal: !ls. h4/bag/BAG__CARD (h4/container/LIST__TO__BAG ls) = h4/list/LENGTH ls
%   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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_arithmetics_ADD1]: !m. h4/num/SUC m = h4/arithmetic/_2B m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_arithmetics_EQu_u_MONOu_u_ADDu_u_EQ]: !p n m. h4/arithmetic/_2B m p = h4/arithmetic/_2B n p <=> m = n
% Assm [h4s_lists_LENGTH0u_c0]: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm [h4s_lists_LENGTH0u_c1]: !t h. h4/list/LENGTH (h4/list/CONS h t) = h4/num/SUC (h4/list/LENGTH t)
% Assm [h4s_lists_listu_u_induction]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (h4/list/CONS h t))) ==> (!l. happ P l)
% Assm [h4s_bags_BAGu_u_CARDu_u_THMu_c0]: h4/bag/BAG__CARD h4/bag/EMPTY__BAG = h4/num/0
% Assm [h4s_bags_BAGu_u_CARDu_u_THMu_c1]: !b. h4/bag/FINITE__BAG b ==> (!e. h4/bag/BAG__CARD (h4/bag/BAG__INSERT e b) = h4/arithmetic/_2B (h4/bag/BAG__CARD b) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_containers_LISTu_u_TOu_u_BAGu_u_defu_c0]: h4/container/LIST__TO__BAG h4/list/NIL = h4/bag/EMPTY__BAG
% Assm [h4s_containers_LISTu_u_TOu_u_BAGu_u_defu_c1]: !t h. h4/container/LIST__TO__BAG (h4/list/CONS h t) = h4/bag/BAG__INSERT h (h4/container/LIST__TO__BAG t)
% Assm [h4s_containers_FINITEu_u_LISTu_u_TOu_u_BAG]: !ls. h4/bag/FINITE__BAG (h4/container/LIST__TO__BAG ls)
% Goal: !ls. h4/bag/BAG__CARD (h4/container/LIST__TO__BAG ls) = h4/list/LENGTH ls
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_Q300161,TV_Q300157]: ![V_f, V_g]: (![V_x]: s(TV_Q300157,happ(s(t_fun(TV_Q300161,TV_Q300157),V_f),s(TV_Q300161,V_x))) = s(TV_Q300157,happ(s(t_fun(TV_Q300161,TV_Q300157),V_g),s(TV_Q300161,V_x))) => s(t_fun(TV_Q300161,TV_Q300157),V_f) = s(t_fun(TV_Q300161,TV_Q300157),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_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> 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_ADD1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_arithmetics_EQu_u_MONOu_u_ADDu_u_EQ, axiom, ![V_p, V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))) <=> s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n))).
fof(ah4s_lists_LENGTH0u_c0, axiom, ![TV_u_27a]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_lists_LENGTH0u_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_listu_u_induction, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_bags_BAGu_u_CARDu_u_THMu_c0, axiom, ![TV_u_27a]: s(t_h4s_nums_num,h4s_bags_bagu_u_card(s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_emptyu_u_bag))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_bags_BAGu_u_CARDu_u_THMu_c1, axiom, ![TV_u_27a]: ![V_b]: (p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b)))) => ![V_e]: s(t_h4s_nums_num,h4s_bags_bagu_u_card(s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(TV_u_27a,V_e),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_bags_bagu_u_card(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))).
fof(ah4s_containers_LISTu_u_TOu_u_BAGu_u_defu_c0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_containers_listu_u_tou_u_bag(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_emptyu_u_bag)).
fof(ah4s_containers_LISTu_u_TOu_u_BAGu_u_defu_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_containers_listu_u_tou_u_bag(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(TV_u_27a,V_h),s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_containers_listu_u_tou_u_bag(s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_containers_FINITEu_u_LISTu_u_TOu_u_BAG, axiom, ![TV_u_27a]: ![V_ls]: p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_containers_listu_u_tou_u_bag(s(t_h4s_lists_list(TV_u_27a),V_ls))))))).
fof(ch4s_containers_CARDu_u_LISTu_u_TOu_u_BAG, conjecture, ![TV_u_27a]: ![V_ls]: s(t_h4s_nums_num,h4s_bags_bagu_u_card(s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_containers_listu_u_tou_u_bag(s(t_h4s_lists_list(TV_u_27a),V_ls))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_ls)))).
