%   ORIGINAL: h4/patricia/PTREE__OF__NUMSET__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/FOLDL0_c0: !f e. h4/list/FOLDL f e h4/list/NIL = e
% Assm: h4/list/SET__TO__LIST__EMPTY: h4/list/SET__TO__LIST h4/pred__set/EMPTY = h4/list/NIL
% Assm: h4/patricia/PTREE__OF__NUMSET__def: !t s. h4/patricia/PTREE__OF__NUMSET t s = h4/list/FOLDL (h4/combin/C h4/patricia/INSERT__PTREE) t (h4/list/SET__TO__LIST s)
% Goal: !t. h4/patricia/PTREE__OF__NUMSET t h4/pred__set/EMPTY = t
%   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_FOLDL0u_c0]: !f e. h4/list/FOLDL f e h4/list/NIL = e
% Assm [h4s_lists_SETu_u_TOu_u_LISTu_u_EMPTY]: h4/list/SET__TO__LIST h4/pred__set/EMPTY = h4/list/NIL
% Assm [h4s_patricias_PTREEu_u_OFu_u_NUMSETu_u_def]: !t s. h4/patricia/PTREE__OF__NUMSET t s = h4/list/FOLDL (h4/combin/C h4/patricia/INSERT__PTREE) t (h4/list/SET__TO__LIST s)
% Goal: !t. h4/patricia/PTREE__OF__NUMSET t h4/pred__set/EMPTY = t
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q287301,TV_Q287297]: ![V_f, V_g]: (![V_x]: s(TV_Q287297,happ(s(t_fun(TV_Q287301,TV_Q287297),V_f),s(TV_Q287301,V_x))) = s(TV_Q287297,happ(s(t_fun(TV_Q287301,TV_Q287297),V_g),s(TV_Q287301,V_x))) => s(t_fun(TV_Q287301,TV_Q287297),V_f) = s(t_fun(TV_Q287301,TV_Q287297),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t0))).
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,t0)))).
fof(ah4s_lists_FOLDL0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_e]: s(TV_u_27b,h4s_lists_foldl(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27b)),V_f),s(TV_u_27b,V_e),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_e)).
fof(ah4s_lists_SETu_u_TOu_u_LISTu_u_EMPTY, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_setu_u_tou_u_list(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_patricias_PTREEu_u_OFu_u_NUMSETu_u_def, axiom, ![V_t, V_s]: s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_ptreeu_u_ofu_u_numset(s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t),s(t_fun(t_h4s_nums_num,t_bool),V_s))) = s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_lists_foldl(s(t_fun(t_h4s_patricias_ptree(t_h4s_ones_one),t_fun(t_h4s_nums_num,t_h4s_patricias_ptree(t_h4s_ones_one))),h4s_combins_c(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(t_h4s_ones_one),t_h4s_patricias_ptree(t_h4s_ones_one))),h4s_patricias_insertu_u_ptree))),s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_setu_u_tou_u_list(s(t_fun(t_h4s_nums_num,t_bool),V_s)))))).
fof(ch4s_patricias_PTREEu_u_OFu_u_NUMSETu_u_EMPTY, conjecture, ![V_t]: s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_ptreeu_u_ofu_u_numset(s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty))) = s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t)).
