%   ORIGINAL: h4/numpair/napp__thm_c1
% 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/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/numpair/ncons__11: !y x t h. h4/numpair/ncons x y = h4/numpair/ncons h t <=> x = h /\ y = t
% Assm: h4/numpair/nlistrec__thm_c1: !t n h f. h4/numpair/nlistrec n f (h4/numpair/ncons h t) = f h t (h4/numpair/nlistrec n f t)
% Assm: h4/numpair/napp__def: !l2 l1. h4/numpair/napp l1 l2 = h4/numpair/nlistrec l2 (\n t r. h4/numpair/ncons n r) l1
% Goal: !t nlist h. h4/numpair/napp (h4/numpair/ncons h t) nlist = h4/numpair/ncons h (h4/numpair/napp t nlist)
%   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_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_numpairs_nconsu_u_11]: !y x t h. h4/numpair/ncons x y = h4/numpair/ncons h t <=> x = h /\ y = t
% Assm [h4s_numpairs_nlistrecu_u_thmu_c1]: !t n h f. h4/numpair/nlistrec n f (h4/numpair/ncons h t) = happ (happ (happ f h) t) (h4/numpair/nlistrec n f t)
% Assm [h4s_numpairs_nappu_u_def]: !_2. (!n r. happ (happ _2 n) r = h4/numpair/ncons n r) ==> (!_1. (!n t. happ (happ _1 n) t = happ _2 n) ==> (!_0. (!n. happ _0 n = happ _1 n) ==> (!l2 l1. h4/numpair/napp l1 l2 = h4/numpair/nlistrec l2 _0 l1)))
% Goal: !t nlist h. h4/numpair/napp (h4/numpair/ncons h t) nlist = h4/numpair/ncons h (h4/numpair/napp t nlist)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q145038,TV_Q145034]: ![V_f, V_g]: (![V_x]: s(TV_Q145034,happ(s(t_fun(TV_Q145038,TV_Q145034),V_f),s(TV_Q145038,V_x))) = s(TV_Q145034,happ(s(t_fun(TV_Q145038,TV_Q145034),V_g),s(TV_Q145038,V_x))) => s(t_fun(TV_Q145038,TV_Q145034),V_f) = s(t_fun(TV_Q145038,TV_Q145034),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t0))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_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,t0)))).
fof(ah4s_numpairs_nconsu_u_11, axiom, ![V_y, V_x, V_t, V_h]: (s(t_h4s_nums_num,h4s_numpairs_ncons(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,h4s_numpairs_ncons(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_t))) <=> (s(t_h4s_nums_num,V_x) = s(t_h4s_nums_num,V_h) & s(t_h4s_nums_num,V_y) = s(t_h4s_nums_num,V_t)))).
fof(ah4s_numpairs_nlistrecu_u_thmu_c1, axiom, ![TV_u_27a]: ![V_t, V_n, V_h, V_f]: s(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_numpairs_ncons(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_t))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),happ(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,V_h))),s(t_h4s_nums_num,V_t))),s(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,V_t)))))).
fof(ah4s_numpairs_nappu_u_def, axiom, ![V_uu_2]: (![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)),V_uu_2),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,V_n),s(t_h4s_nums_num,V_r))) => ![V_uu_1]: (![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))),V_uu_1),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)),V_uu_2),s(t_h4s_nums_num,V_n))) => ![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)),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_1),s(t_h4s_nums_num,V_n))) => ![V_l2, V_l1]: s(t_h4s_nums_num,h4s_numpairs_napp(s(t_h4s_nums_num,V_l1),s(t_h4s_nums_num,V_l2))) = s(t_h4s_nums_num,h4s_numpairs_nlistrec(s(t_h4s_nums_num,V_l2),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_l1))))))).
fof(ch4s_numpairs_nappu_u_thmu_c1, conjecture, ![V_t, V_nlist, V_h]: s(t_h4s_nums_num,h4s_numpairs_napp(s(t_h4s_nums_num,h4s_numpairs_ncons(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_t))),s(t_h4s_nums_num,V_nlist))) = s(t_h4s_nums_num,h4s_numpairs_ncons(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,h4s_numpairs_napp(s(t_h4s_nums_num,V_t),s(t_h4s_nums_num,V_nlist)))))).
