%   ORIGINAL: h4/numpair/nmap__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/nmap__def: !f. h4/numpair/nmap f = h4/numpair/nlistrec h4/num/0 (\n t r. h4/numpair/ncons (f n) r)
% Goal: !t h f. h4/numpair/nmap f (h4/numpair/ncons h t) = h4/numpair/ncons (f h) (h4/numpair/nmap f t)
%   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. happ (h4/numpair/nlistrec n f) (h4/numpair/ncons h t) = happ (happ (happ f h) t) (happ (h4/numpair/nlistrec n f) t)
% 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: !t h f. happ (h4/numpair/nmap f) (h4/numpair/ncons h t) = h4/numpair/ncons (happ f h) (happ (h4/numpair/nmap f) t)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q144938,TV_Q144934]: ![V_f, V_g]: (![V_x]: s(TV_Q144934,happ(s(t_fun(TV_Q144938,TV_Q144934),V_f),s(TV_Q144938,V_x))) = s(TV_Q144934,happ(s(t_fun(TV_Q144938,TV_Q144934),V_g),s(TV_Q144938,V_x))) => s(t_fun(TV_Q144938,TV_Q144934),V_f) = s(t_fun(TV_Q144938,TV_Q144934),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,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_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,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,V_t)))))).
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_c1, conjecture, ![V_t, V_h, 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_numpairs_ncons(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_t))))) = 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_h))),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,V_t)))))).
