%   ORIGINAL: h4/patricia/NUMSET__OF__PTREE__EMPTY
% 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/LIST__TO__SET__THM_c0: h4/list/LIST__TO__SET h4/list/NIL = h4/pred__set/EMPTY
% Assm: h4/patricia/TRAVERSE__def_c0: h4/patricia/TRAVERSE h4/patricia/Empty = h4/list/NIL
% Assm: h4/patricia/NUMSET__OF__PTREE__def: !t. h4/patricia/NUMSET__OF__PTREE t = h4/list/LIST__TO__SET (h4/patricia/TRAVERSE t)
% Goal: h4/patricia/NUMSET__OF__PTREE h4/patricia/Empty = h4/pred__set/EMPTY
%   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_LISTu_u_TOu_u_SETu_u_THMu_c0]: h4/list/LIST__TO__SET h4/list/NIL = h4/pred__set/EMPTY
% Assm [h4s_patricias_TRAVERSEu_u_defu_c0]: h4/patricia/TRAVERSE h4/patricia/Empty = h4/list/NIL
% Assm [h4s_patricias_NUMSETu_u_OFu_u_PTREEu_u_def]: !t. h4/patricia/NUMSET__OF__PTREE t = h4/list/LIST__TO__SET (h4/patricia/TRAVERSE t)
% Goal: h4/patricia/NUMSET__OF__PTREE h4/patricia/Empty = h4/pred__set/EMPTY
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_Q287276,TV_Q287272]: ![V_f, V_g]: (![V_x]: s(TV_Q287272,happ(s(t_fun(TV_Q287276,TV_Q287272),V_f),s(TV_Q287276,V_x))) = s(TV_Q287272,happ(s(t_fun(TV_Q287276,TV_Q287272),V_g),s(TV_Q287276,V_x))) => s(t_fun(TV_Q287276,TV_Q287272),V_f) = s(t_fun(TV_Q287276,TV_Q287272),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_LISTu_u_TOu_u_SETu_u_THMu_c0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)).
fof(ah4s_patricias_TRAVERSEu_u_defu_c0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_empty))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_nil)).
fof(ah4s_patricias_NUMSETu_u_OFu_u_PTREEu_u_def, axiom, ![V_t]: s(t_fun(t_h4s_nums_num,t_bool),h4s_patricias_numsetu_u_ofu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t)))))).
fof(ch4s_patricias_NUMSETu_u_OFu_u_PTREEu_u_EMPTY, conjecture, s(t_fun(t_h4s_nums_num,t_bool),h4s_patricias_numsetu_u_ofu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_empty))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty)).
