%   ORIGINAL: h4/rich__list/BUTLASTN__LENGTH__CONS
% 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/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/arithmetic/LESS__EQ__REFL: !m. h4/arithmetic/_3C_3D m m
% Assm: h4/rich__list/BUTLASTN__LENGTH__NIL0: !l. h4/rich__list/BUTLASTN (h4/list/LENGTH l) l = h4/list/NIL
% Assm: h4/rich__list/BUTLASTN__CONS: !n l. h4/arithmetic/_3C_3D n (h4/list/LENGTH l) ==> (!x. h4/rich__list/BUTLASTN n (h4/list/CONS x l) = h4/list/CONS x (h4/rich__list/BUTLASTN n l))
% Goal: !x l. h4/rich__list/BUTLASTN (h4/list/LENGTH l) (h4/list/CONS x l) = h4/list/CONS x h4/list/NIL
%   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_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_arithmetics_LESSu_u_EQu_u_REFL]: !m. h4/arithmetic/_3C_3D m m
% Assm [h4s_richu_u_lists_BUTLASTNu_u_LENGTHu_u_NIL0]: !l. h4/rich__list/BUTLASTN (h4/list/LENGTH l) l = h4/list/NIL
% Assm [h4s_richu_u_lists_BUTLASTNu_u_CONS]: !n l. h4/arithmetic/_3C_3D n (h4/list/LENGTH l) ==> (!x. h4/rich__list/BUTLASTN n (h4/list/CONS x l) = h4/list/CONS x (h4/rich__list/BUTLASTN n l))
% Goal: !x l. h4/rich__list/BUTLASTN (h4/list/LENGTH l) (h4/list/CONS x l) = h4/list/CONS x h4/list/NIL
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_Q160733,TV_Q160729]: ![V_f, V_g]: (![V_x]: s(TV_Q160729,happ(s(t_fun(TV_Q160733,TV_Q160729),V_f),s(TV_Q160733,V_x))) = s(TV_Q160729,happ(s(t_fun(TV_Q160733,TV_Q160729),V_g),s(TV_Q160733,V_x))) => s(t_fun(TV_Q160733,TV_Q160729),V_f) = s(t_fun(TV_Q160733,TV_Q160729),V_g))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_REFL, axiom, ![V_m]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_m))))).
fof(ah4s_richu_u_lists_BUTLASTNu_u_LENGTHu_u_NIL0, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_butlastn(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_richu_u_lists_BUTLASTNu_u_CONS, axiom, ![TV_u_27a]: ![V_n, V_l]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => ![V_x]: s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_butlastn(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_butlastn(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_l))))))).
fof(ch4s_richu_u_lists_BUTLASTNu_u_LENGTHu_u_CONS, conjecture, ![TV_u_27a]: ![V_x, V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_butlastn(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))).
