%   ORIGINAL: h4/numpair/nmap__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/nmap__def: !f. h4/numpair/nmap f = h4/numpair/nlistrec h4/num/0 (\n t r. h4/numpair/ncons (f n) r)
% Goal: !f. h4/numpair/nmap f 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_nmapu_u_def]: !_2. (!f n r. happ (happ (happ _2 f) n) r = h4/numpair/ncons (happ f n) r) ==> (!_1. (!f n t. happ (happ (happ _1 f) n) t = happ (happ _2 f) n) ==> (!_0. (!f n. happ (happ _0 f) n = happ (happ _1 f) n) ==> (!f. h4/numpair/nmap f = h4/numpair/nlistrec h4/num/0 (happ _0 f))))
% Goal: !f. happ (h4/numpair/nmap f) h4/num/0 = h4/num/0
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q144913,TV_Q144909]: ![V_f, V_g]: (![V_x]: s(TV_Q144909,happ(s(t_fun(TV_Q144913,TV_Q144909),V_f),s(TV_Q144913,V_x))) = s(TV_Q144909,happ(s(t_fun(TV_Q144913,TV_Q144909),V_g),s(TV_Q144913,V_x))) => s(t_fun(TV_Q144913,TV_Q144909),V_f) = s(t_fun(TV_Q144913,TV_Q144909),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_nmapu_u_def, axiom, ![V_uu_2]: (![V_f, V_n, V_r]: s(t_h4s_nums_num,happ(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)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),V_uu_2),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),V_f))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_r))) = s(t_h4s_nums_num,h4s_numpairs_ncons(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),V_f),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_r))) => ![V_uu_1]: (![V_f, V_n, 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)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_nums_num,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),V_f))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,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)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),V_uu_2),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),V_f))),s(t_h4s_nums_num,V_n))) => ![V_uu_0]: (![V_f, 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))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_nums_num),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_fun(t_h4s_nums_num,t_h4s_nums_num),V_f))),s(t_h4s_nums_num,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))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_nums_num,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),V_f))),s(t_h4s_nums_num,V_n))) => ![V_f]: s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numpairs_nmap(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),V_f))) = 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))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_nums_num),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_fun(t_h4s_nums_num,t_h4s_nums_num),V_f))))))))).
fof(ch4s_numpairs_nmapu_u_thmu_c0, conjecture, ![V_f]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numpairs_nmap(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),V_f))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_nums_0)).
