%   ORIGINAL: h4/rich__list/ELL__SUC__SNOC
% 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/prim__rec/LESS__0: !n. h4/prim__rec/_3C h4/num/0 (h4/num/SUC n)
% Assm: h4/prim__rec/PRE0_c1: !m. h4/prim__rec/PRE (h4/num/SUC m) = m
% Assm: h4/rich__list/ELL__SNOC: !n. h4/prim__rec/_3C h4/num/0 n ==> (!x l. h4/rich__list/ELL n (h4/list/SNOC x l) = h4/rich__list/ELL (h4/prim__rec/PRE n) l)
% Goal: !x n l. h4/rich__list/ELL (h4/num/SUC n) (h4/list/SNOC x l) = h4/rich__list/ELL n l
%   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_primu_u_recs_LESSu_u_0]: !n. h4/prim__rec/_3C h4/num/0 (h4/num/SUC n)
% Assm [h4s_primu_u_recs_PRE0u_c1]: !m. h4/prim__rec/PRE (h4/num/SUC m) = m
% Assm [h4s_richu_u_lists_ELLu_u_SNOC]: !n. h4/prim__rec/_3C h4/num/0 n ==> (!x l. h4/rich__list/ELL n (h4/list/SNOC x l) = h4/rich__list/ELL (h4/prim__rec/PRE n) l)
% Goal: !x n l. h4/rich__list/ELL (h4/num/SUC n) (h4/list/SNOC x l) = h4/rich__list/ELL n l
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_Q161883,TV_Q161879]: ![V_f, V_g]: (![V_x]: s(TV_Q161879,happ(s(t_fun(TV_Q161883,TV_Q161879),V_f),s(TV_Q161883,V_x))) = s(TV_Q161879,happ(s(t_fun(TV_Q161883,TV_Q161879),V_g),s(TV_Q161883,V_x))) => s(t_fun(TV_Q161883,TV_Q161879),V_f) = s(t_fun(TV_Q161883,TV_Q161879),V_g))).
fof(ah4s_primu_u_recs_LESSu_u_0, axiom, ![V_n]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))))).
fof(ah4s_primu_u_recs_PRE0u_c1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_richu_u_lists_ELLu_u_SNOC, axiom, ![TV_u_27a]: ![V_n]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n)))) => ![V_x, V_l]: s(TV_u_27a,h4s_richu_u_lists_ell(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(TV_u_27a,h4s_richu_u_lists_ell(s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),V_l))))).
fof(ch4s_richu_u_lists_ELLu_u_SUCu_u_SNOC, conjecture, ![TV_u_27a]: ![V_x, V_n, V_l]: s(TV_u_27a,h4s_richu_u_lists_ell(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(TV_u_27a,h4s_richu_u_lists_ell(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_l)))).
