%   ORIGINAL: h4/rich__list/ELL__0__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/bool/TRUTH: T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/list/LAST__SNOC: !x l. h4/list/LAST (h4/list/SNOC x l) = x
% Assm: h4/rich__list/ELL0_c0: !l. h4/rich__list/ELL h4/num/0 l = h4/list/LAST l
% Goal: !x l. h4/rich__list/ELL h4/num/0 (h4/list/SNOC x l) = x
%   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_lists_LASTu_u_SNOC]: !x l. h4/list/LAST (h4/list/SNOC x l) = x
% Assm [h4s_richu_u_lists_ELL0u_c0]: !l. h4/rich__list/ELL h4/num/0 l = h4/list/LAST l
% Goal: !x l. h4/rich__list/ELL h4/num/0 (h4/list/SNOC x l) = x
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_Q161833,TV_Q161829]: ![V_f, V_g]: (![V_x]: s(TV_Q161829,happ(s(t_fun(TV_Q161833,TV_Q161829),V_f),s(TV_Q161833,V_x))) = s(TV_Q161829,happ(s(t_fun(TV_Q161833,TV_Q161829),V_g),s(TV_Q161833,V_x))) => s(t_fun(TV_Q161833,TV_Q161829),V_f) = s(t_fun(TV_Q161833,TV_Q161829),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,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_lists_LASTu_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_l]: s(TV_u_27a,h4s_lists_last(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,V_x)).
fof(ah4s_richu_u_lists_ELL0u_c0, axiom, ![TV_u_27a]: ![V_l]: s(TV_u_27a,h4s_richu_u_lists_ell(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(TV_u_27a,h4s_lists_last(s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ch4s_richu_u_lists_ELLu_u_0u_u_SNOC, conjecture, ![TV_u_27a]: ![V_x, V_l]: s(TV_u_27a,h4s_richu_u_lists_ell(s(t_h4s_nums_num,h4s_nums_0),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,V_x)).
