%   ORIGINAL: h4/list/GENLIST__PLUS__APPEND
% 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/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/BOUNDED__THM: !v. h4/bool/BOUNDED v <=> T
% Assm: h4/marker/Cong__def: !x. h4/marker/Cong x <=> x
% Assm: h4/num/INDUCTION: !P. P h4/num/0 /\ (!n. P n ==> P (h4/num/SUC n)) ==> (!n. P n)
% Assm: h4/arithmetic/ADD_c0: !n. h4/arithmetic/_2B h4/num/0 n = n
% Assm: h4/arithmetic/ADD_c1: !n m. h4/arithmetic/_2B (h4/num/SUC m) n = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm: h4/arithmetic/ADD__0: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/arithmetic/ADD__SUC: !n m. h4/num/SUC (h4/arithmetic/_2B m n) = h4/arithmetic/_2B m (h4/num/SUC n)
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/list/GENLIST__APPEND: !f b a. h4/list/GENLIST f (h4/arithmetic/_2B a b) = h4/list/APPEND (h4/list/GENLIST f b) (h4/list/GENLIST (\t. f (h4/arithmetic/_2B t b)) a)
% Goal: !n2 n1 a. h4/list/APPEND (h4/list/GENLIST (h4/arithmetic/_2B a) n1) (h4/list/GENLIST (h4/arithmetic/_2B (h4/arithmetic/_2B n1 a)) n2) = h4/list/GENLIST (h4/arithmetic/_2B a) (h4/arithmetic/_2B n1 n2)
%   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_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_BOUNDEDu_u_THM]: !v. h4/bool/BOUNDED v <=> T
% Assm [h4s_markers_Congu_u_def]: !x. h4/marker/Cong x <=> x
% Assm [h4s_nums_INDUCTION]: !P. happ P h4/num/0 /\ (!n. happ P n ==> happ P (h4/num/SUC n)) ==> (!n. happ P n)
% Assm [h4s_arithmetics_ADDu_c0]: !n. happ (h4/arithmetic/_2B h4/num/0) n = n
% Assm [h4s_arithmetics_ADDu_c1]: !n m. happ (h4/arithmetic/_2B (h4/num/SUC m)) n = h4/num/SUC (happ (h4/arithmetic/_2B m) n)
% Assm [h4s_arithmetics_ADDu_u_0]: !m. happ (h4/arithmetic/_2B m) h4/num/0 = m
% Assm [h4s_arithmetics_ADDu_u_SUC]: !n m. h4/num/SUC (happ (h4/arithmetic/_2B m) n) = happ (h4/arithmetic/_2B m) (h4/num/SUC n)
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. happ (h4/arithmetic/_2B m) n = happ (h4/arithmetic/_2B n) m
% Assm [h4s_arithmetics_ADDu_u_ASSOC]: !p n m. happ (h4/arithmetic/_2B m) (happ (h4/arithmetic/_2B n) p) = happ (h4/arithmetic/_2B (happ (h4/arithmetic/_2B m) n)) p
% Assm [h4s_lists_GENLISTu_u_APPEND]: !_0. (!f b t. happ (happ (happ _0 f) b) t = happ f (happ (h4/arithmetic/_2B t) b)) ==> (!f b a. h4/list/GENLIST f (happ (h4/arithmetic/_2B a) b) = h4/list/APPEND (h4/list/GENLIST f b) (h4/list/GENLIST (happ (happ _0 f) b) a))
% Goal: !n2 n1 a. h4/list/APPEND (h4/list/GENLIST (h4/arithmetic/_2B a) n1) (h4/list/GENLIST (h4/arithmetic/_2B (happ (h4/arithmetic/_2B n1) a)) n2) = h4/list/GENLIST (h4/arithmetic/_2B a) (happ (h4/arithmetic/_2B n1) n2)
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_Q248953,TV_Q248949]: ![V_f, V_g]: (![V_x]: s(TV_Q248949,happ(s(t_fun(TV_Q248953,TV_Q248949),V_f),s(TV_Q248953,V_x))) = s(TV_Q248949,happ(s(t_fun(TV_Q248953,TV_Q248949),V_g),s(TV_Q248953,V_x))) => s(t_fun(TV_Q248953,TV_Q248949),V_f) = s(t_fun(TV_Q248953,TV_Q248949),V_g))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: 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,t)))).
fof(ah4s_bools_BOUNDEDu_u_THM, axiom, ![V_v]: s(t_bool,h4s_bools_bounded(s(t_bool,V_v))) = s(t_bool,t)).
fof(ah4s_markers_Congu_u_def, axiom, ![V_x]: s(t_bool,h4s_markers_cong(s(t_bool,V_x))) = s(t_bool,V_x)).
fof(ah4s_nums_INDUCTION, axiom, ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_0)))) & ![V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))))) => ![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_ADDu_c0, axiom, ![V_n]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_ADDu_c1, axiom, ![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_ADDu_u_0, axiom, ![V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_SUC, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_ADDu_u_COMM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,V_p)))).
fof(ah4s_lists_GENLISTu_u_APPEND, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_f, V_b, V_t]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,TV_u_27a))),V_uu_0),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,V_b))),s(t_h4s_nums_num,V_t))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_t))),s(t_h4s_nums_num,V_b))))) => ![V_f, V_b, V_a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,V_b))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_b))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,TV_u_27a))),V_uu_0),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,V_b))),s(t_h4s_nums_num,V_a))))))).
fof(ch4s_lists_GENLISTu_u_PLUSu_u_APPEND, conjecture, ![V_n2, V_n1, V_a]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_append(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,V_n1))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n1))),s(t_h4s_nums_num,V_a))))),s(t_h4s_nums_num,V_n2))))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n1))),s(t_h4s_nums_num,V_n2)))))).
