%   ORIGINAL: h4/list/LENGTH__LEN
% 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/list/LEN__LENGTH__LEM: !n L. h4/list/LEN L n = h4/arithmetic/_2B (h4/list/LENGTH L) n
% Goal: !L. h4/list/LENGTH L = h4/list/LEN L h4/num/0
%   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_lists_LENu_u_LENGTHu_u_LEM]: !n L. h4/list/LEN L n = h4/arithmetic/_2B (h4/list/LENGTH L) n
% Goal: !L. h4/list/LENGTH L = h4/list/LEN L h4/num/0
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_Q246659,TV_Q246655]: ![V_f, V_g]: (![V_x]: s(TV_Q246655,happ(s(t_fun(TV_Q246659,TV_Q246655),V_f),s(TV_Q246659,V_x))) = s(TV_Q246655,happ(s(t_fun(TV_Q246659,TV_Q246655),V_g),s(TV_Q246659,V_x))) => s(t_fun(TV_Q246659,TV_Q246655),V_f) = s(t_fun(TV_Q246659,TV_Q246655),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_lists_LENu_u_LENGTHu_u_LEM, axiom, ![TV_u_27a]: ![V_n, V_L]: s(t_h4s_nums_num,h4s_lists_len(s(t_h4s_lists_list(TV_u_27a),V_L),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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)))).
fof(ch4s_lists_LENGTHu_u_LEN, conjecture, ![TV_u_27a]: ![V_L]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_L))) = s(t_h4s_nums_num,h4s_lists_len(s(t_h4s_lists_list(TV_u_27a),V_L),s(t_h4s_nums_num,h4s_nums_0)))).
