%   ORIGINAL: h4/bitstring/length__bitify__null
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/arithmetic/ADD__0: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/list/LENGTH0_c0: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm: h4/bitstring/length__bitify: !v l. h4/list/LENGTH (h4/bitstring/bitify l v) = h4/arithmetic/_2B (h4/list/LENGTH l) (h4/list/LENGTH v)
% Goal: !v. h4/list/LENGTH (h4/bitstring/bitify h4/list/NIL v) = h4/list/LENGTH v
%   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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_arithmetics_ADDu_u_0]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_lists_LENGTH0u_c0]: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm [h4s_bitstrings_lengthu_u_bitify]: !v l. h4/list/LENGTH (h4/bitstring/bitify l v) = h4/arithmetic/_2B (h4/list/LENGTH l) (h4/list/LENGTH v)
% Goal: !v. h4/list/LENGTH (h4/bitstring/bitify h4/list/NIL v) = h4/list/LENGTH v
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_Q88129,TV_Q88125]: ![V_f, V_g]: (![V_x]: s(TV_Q88125,happ(s(t_fun(TV_Q88129,TV_Q88125),V_f),s(TV_Q88129,V_x))) = s(TV_Q88125,happ(s(t_fun(TV_Q88129,TV_Q88125),V_g),s(TV_Q88129,V_x))) => s(t_fun(TV_Q88129,TV_Q88125),V_f) = s(t_fun(TV_Q88129,TV_Q88125),V_g))).
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_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_arithmetics_ADDu_u_SYM, axiom, ![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_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
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_bitstrings_lengthu_u_bitify, axiom, ![V_v, V_l]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_nums_num),h4s_bitstrings_bitify(s(t_h4s_lists_list(t_h4s_nums_num),V_l),s(t_h4s_lists_list(t_bool),V_v))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_nums_num),V_l))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_v)))))).
fof(ch4s_bitstrings_lengthu_u_bitifyu_u_null, conjecture, ![V_v]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_nums_num),h4s_bitstrings_bitify(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_nil),s(t_h4s_lists_list(t_bool),V_v))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_v)))).
