%   ORIGINAL: h4/bag/EMPTY__BAG__alt
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/FUN__EQ__THM: !g f. f = g <=> (!x. f x = g x)
% Assm: h4/combin/K__THM: !y x. h4/combin/K x y = x
% Assm: h4/bag/EMPTY__BAG0: h4/bag/EMPTY__BAG = h4/combin/K h4/num/0
% Goal: h4/bag/EMPTY__BAG = (\x. h4/num/0)
%   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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_FUNu_u_EQu_u_THM]: !g f. f = g <=> (!x. happ f x = happ g x)
% Assm [h4s_combins_Ku_u_THM]: !y x. happ (h4/combin/K x) y = x
% Assm [h4s_bags_EMPTYu_u_BAG0]: h4/bag/EMPTY__BAG = h4/combin/K h4/num/0
% Goal: !x. happ h4/bag/EMPTY__BAG x = h4/num/0
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_Q226708,TV_Q226704]: ![V_f, V_g]: (![V_x]: s(TV_Q226704,happ(s(t_fun(TV_Q226708,TV_Q226704),V_f),s(TV_Q226708,V_x))) = s(TV_Q226704,happ(s(t_fun(TV_Q226708,TV_Q226704),V_g),s(TV_Q226708,V_x))) => s(t_fun(TV_Q226708,TV_Q226704),V_f) = s(t_fun(TV_Q226708,TV_Q226704),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_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_bools_FUNu_u_EQu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_g, V_f]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),V_g) <=> ![V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_g),s(TV_u_27a,V_x))))).
fof(ah4s_combins_Ku_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),h4s_combins_k(s(TV_u_27a,V_x))),s(TV_u_27b,V_y))) = s(TV_u_27a,V_x)).
fof(ah4s_bags_EMPTYu_u_BAG0, axiom, ![TV_u_27a]: 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),h4s_combins_k(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ch4s_bags_EMPTYu_u_BAGu_u_alt, conjecture, ![TV_u_27a]: ![V_x]: s(t_h4s_nums_num,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_emptyu_u_bag),s(TV_u_27a,V_x))) = s(t_h4s_nums_num,h4s_nums_0)).
