%   ORIGINAL: h4/patricia/FINITE__NUMSET__OF__PTREE
% 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/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/list/FINITE__LIST__TO__SET: !l. h4/pred__set/FINITE (h4/list/LIST__TO__SET l)
% Assm: h4/patricia/NUMSET__OF__PTREE__def: !t. h4/patricia/NUMSET__OF__PTREE t = h4/list/LIST__TO__SET (h4/patricia/TRAVERSE t)
% Goal: !t. h4/pred__set/FINITE (h4/patricia/NUMSET__OF__PTREE 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_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_lists_FINITEu_u_LISTu_u_TOu_u_SET]: !l. h4/pred__set/FINITE (h4/list/LIST__TO__SET l)
% 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: !t. h4/pred__set/FINITE (h4/patricia/NUMSET__OF__PTREE 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_Q286997,TV_Q286993]: ![V_f, V_g]: (![V_x]: s(TV_Q286993,happ(s(t_fun(TV_Q286997,TV_Q286993),V_f),s(TV_Q286997,V_x))) = s(TV_Q286993,happ(s(t_fun(TV_Q286997,TV_Q286993),V_g),s(TV_Q286997,V_x))) => s(t_fun(TV_Q286997,TV_Q286993),V_f) = s(t_fun(TV_Q286997,TV_Q286993),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t0))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) <=> p(s(t_bool,V_t)))).
fof(ah4s_lists_FINITEu_u_LISTu_u_TOu_u_SET, axiom, ![TV_u_27a]: ![V_l]: p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l))))))).
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_FINITEu_u_NUMSETu_u_OFu_u_PTREE, conjecture, ![V_t]: p(s(t_bool,h4s_predu_u_sets_finite(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))))))).
