%   ORIGINAL: h4/path/PL__thm_c0
% 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/path/PL__stopped__at: !x. h4/path/PL (h4/path/stopped__at x) = h4/pred__set/INSERT h4/num/0 h4/pred__set/EMPTY
% Goal: !x. h4/path/PL (h4/path/stopped__at x) = h4/pred__set/INSERT h4/num/0 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_paths_PLu_u_stoppedu_u_at]: !x. h4/path/PL (h4/path/stopped__at x) = h4/pred__set/INSERT h4/num/0 h4/pred__set/EMPTY
% Goal: !x. h4/path/PL (h4/path/stopped__at x) = h4/pred__set/INSERT h4/num/0 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_Q141604,TV_Q141600]: ![V_f, V_g]: (![V_x]: s(TV_Q141600,happ(s(t_fun(TV_Q141604,TV_Q141600),V_f),s(TV_Q141604,V_x))) = s(TV_Q141600,happ(s(t_fun(TV_Q141604,TV_Q141600),V_g),s(TV_Q141604,V_x))) => s(t_fun(TV_Q141604,TV_Q141600),V_f) = s(t_fun(TV_Q141604,TV_Q141600),V_g))).
fof(ah4s_paths_PLu_u_stoppedu_u_at, axiom, ![TV_u_27b,TV_u_27a]: ![V_x]: s(t_fun(t_h4s_nums_num,t_bool),h4s_paths_pl(s(t_h4s_paths_path(TV_u_27a,TV_u_27b),h4s_paths_stoppedu_u_at(s(TV_u_27a,V_x))))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_insert(s(t_h4s_nums_num,h4s_nums_0),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty)))).
fof(ch4s_paths_PLu_u_thmu_c0, conjecture, ![TV_u_27b,TV_u_27a]: ![V_x]: s(t_fun(t_h4s_nums_num,t_bool),h4s_paths_pl(s(t_h4s_paths_path(TV_u_27a,TV_u_27b),h4s_paths_stoppedu_u_at(s(TV_u_27a,V_x))))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_insert(s(t_h4s_nums_num,h4s_nums_0),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty)))).
