%   ORIGINAL: h4/numpair/nlen__thm_c0
% 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/numpair/nlistrec__thm_c0: !n f. h4/numpair/nlistrec n f h4/num/0 = n
% Assm: h4/numpair/nlen__def: h4/numpair/nlen = h4/numpair/nlistrec h4/num/0 (\n t r. h4/arithmetic/_2B r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Goal: h4/numpair/nlen h4/num/0 = 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_numpairs_nlistrecu_u_thmu_c0]: !n f. happ (h4/numpair/nlistrec n f) h4/num/0 = n
% Assm [h4s_numpairs_nlenu_u_def]: !_2. (!r. happ _2 r = h4/arithmetic/_2B r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) ==> (!_1. (!t. happ _1 t = _2) ==> (!_0. (!n. happ _0 n = _1) ==> h4/numpair/nlen = h4/numpair/nlistrec h4/num/0 _0))
% Goal: happ h4/numpair/nlen h4/num/0 = 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_Q144863,TV_Q144859]: ![V_f, V_g]: (![V_x]: s(TV_Q144859,happ(s(t_fun(TV_Q144863,TV_Q144859),V_f),s(TV_Q144863,V_x))) = s(TV_Q144859,happ(s(t_fun(TV_Q144863,TV_Q144859),V_g),s(TV_Q144863,V_x))) => s(t_fun(TV_Q144863,TV_Q144859),V_f) = s(t_fun(TV_Q144863,TV_Q144859),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_numpairs_nlistrecu_u_thmu_c0, axiom, ![TV_u_27a]: ![V_n, V_f]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_numpairs_nlistrec(s(TV_u_27a,V_n),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),V_f))),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,V_n)).
fof(ah4s_numpairs_nlenu_u_def, axiom, ![V_uu_2]: (![V_r]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),V_uu_2),s(t_h4s_nums_num,V_r))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_r),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) => ![V_uu_1]: (![V_t]: s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_t))) = s(t_fun(t_h4s_nums_num,t_h4s_nums_num),V_uu_2) => ![V_uu_0]: (![V_n]: s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1) => s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numpairs_nlen) = s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numpairs_nlistrec(s(t_h4s_nums_num,h4s_nums_0),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),V_uu_0))))))).
fof(ch4s_numpairs_nlenu_u_thmu_c0, conjecture, s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numpairs_nlen),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_nums_0)).
