%   ORIGINAL: h4/extended__emit/SUB__BAG__EQNS_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/bool/TRUTH: T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bag/SUB__BAG__EMPTY_c0: !b. h4/bag/SUB__BAG h4/bag/EMPTY__BAG b
% Goal: !b. h4/bag/SUB__BAG h4/bag/EMPTY__BAG b <=> 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_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bags_SUBu_u_BAGu_u_EMPTYu_c0]: !b. h4/bag/SUB__BAG h4/bag/EMPTY__BAG b
% Goal: !b. h4/bag/SUB__BAG h4/bag/EMPTY__BAG b <=> T
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_Q266637,TV_Q266633]: ![V_f, V_g]: (![V_x]: s(TV_Q266633,happ(s(t_fun(TV_Q266637,TV_Q266633),V_f),s(TV_Q266637,V_x))) = s(TV_Q266633,happ(s(t_fun(TV_Q266637,TV_Q266633),V_g),s(TV_Q266637,V_x))) => s(t_fun(TV_Q266637,TV_Q266633),V_f) = s(t_fun(TV_Q266637,TV_Q266633),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bags_SUBu_u_BAGu_u_EMPTYu_c0, axiom, ![TV_u_27a]: ![V_b]: p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_emptyu_u_bag),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b))))).
fof(ch4s_extendedu_u_emits_SUBu_u_BAGu_u_EQNSu_c0, conjecture, ![TV_u_27a]: ![V_b]: s(t_bool,h4s_bags_subu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_emptyu_u_bag),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b))) = s(t_bool,t)).
