%   ORIGINAL: h4/numpair/nfoldl__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/REFL__CLAUSE: !x. x = x <=> 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/nfoldl__def: !l f a. h4/numpair/nfoldl f a l = h4/numpair/nlistrec (\a0. a0) (\n t r a0. r (f n a0)) l a
% Goal: !t h f a. h4/numpair/nfoldl f a (h4/numpair/ncons h t) = h4/numpair/nfoldl f (f h a) 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_REFLu_u_CLAUSE]: !x. x = x <=> 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_nfoldlu_u_def]: !_4. (!r f n a0. happ (happ (happ (happ _4 r) f) n) a0 = happ r (happ (happ f n) a0)) ==> (!_3. (!f n r. happ (happ (happ _3 f) n) r = happ (happ (happ _4 r) f) n) ==> (!_2. (!f n t. happ (happ (happ _2 f) n) t = happ (happ _3 f) n) ==> (!_1. (!f n. happ (happ _1 f) n = happ (happ _2 f) n) ==> (!_0. (!a0. happ _0 a0 = a0) ==> (!l f a. h4/numpair/nfoldl f a l = happ (h4/numpair/nlistrec _0 (happ _1 f) l) a)))))
% Goal: !t h f a. h4/numpair/nfoldl f a (h4/numpair/ncons h t) = h4/numpair/nfoldl f (happ (happ f h) a) 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_Q144988,TV_Q144984]: ![V_f, V_g]: (![V_x]: s(TV_Q144984,happ(s(t_fun(TV_Q144988,TV_Q144984),V_f),s(TV_Q144988,V_x))) = s(TV_Q144984,happ(s(t_fun(TV_Q144988,TV_Q144984),V_g),s(TV_Q144988,V_x))) => s(t_fun(TV_Q144988,TV_Q144984),V_f) = s(t_fun(TV_Q144988,TV_Q144984),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t0))).
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_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_nfoldlu_u_def, axiom, ![TV_u_27a]: ![V_uu_4]: (![V_r, V_f, V_n, V_a0]: 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_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)))),V_uu_4),s(t_fun(TV_u_27a,TV_u_27a),V_r))),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),V_f))),s(t_h4s_nums_num,V_n))),s(TV_u_27a,V_a0))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_r),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)),V_f),s(t_h4s_nums_num,V_n))),s(TV_u_27a,V_a0))))) => ![V_uu_3]: (![V_f, V_n, V_r]: s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a)))),V_uu_3),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),V_f))),s(t_h4s_nums_num,V_n))),s(t_fun(TV_u_27a,TV_u_27a),V_r))) = 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_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)))),V_uu_4),s(t_fun(TV_u_27a,TV_u_27a),V_r))),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),V_f))),s(t_h4s_nums_num,V_n))) => ![V_uu_2]: (![V_f, V_n, V_t]: s(t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a))))),V_uu_2),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),V_f))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_t))) = s(t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a)))),V_uu_3),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),V_f))),s(t_h4s_nums_num,V_n))) => ![V_uu_1]: (![V_f, V_n]: s(t_fun(t_h4s_nums_num,t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a))))),V_uu_1),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),V_f))),s(t_h4s_nums_num,V_n))) = s(t_fun(t_h4s_nums_num,t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a))))),V_uu_2),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),V_f))),s(t_h4s_nums_num,V_n))) => ![V_uu_0]: (![V_a0]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_uu_0),s(TV_u_27a,V_a0))) = s(TV_u_27a,V_a0) => ![V_l, V_f, V_a]: s(TV_u_27a,h4s_numpairs_nfoldl(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_a),s(t_h4s_nums_num,V_l))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),h4s_numpairs_nlistrec(s(t_fun(TV_u_27a,TV_u_27a),V_uu_0),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(TV_u_27a,TV_u_27a),t_fun(TV_u_27a,TV_u_27a))))),V_uu_1),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),V_f))),s(t_h4s_nums_num,V_l))),s(TV_u_27a,V_a))))))))).
fof(ch4s_numpairs_nfoldlu_u_thmu_c1, conjecture, ![TV_u_27a]: ![V_t, V_h, V_f, V_a]: s(TV_u_27a,h4s_numpairs_nfoldl(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_a),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,h4s_numpairs_nfoldl(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),V_f),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)),V_f),s(t_h4s_nums_num,V_h))),s(TV_u_27a,V_a))),s(t_h4s_nums_num,V_t)))).
