%   ORIGINAL: h4/bag/SET__OF__EL__BAG
% 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/bag/EL__BAG0: !e. h4/bag/EL__BAG e = h4/bag/BAG__INSERT e h4/bag/EMPTY__BAG
% Assm: h4/bag/BAG__OF__EMPTY: h4/bag/SET__OF__BAG h4/bag/EMPTY__BAG = h4/pred__set/EMPTY
% Assm: h4/bag/SET__OF__BAG__INSERT: !e b. h4/bag/SET__OF__BAG (h4/bag/BAG__INSERT e b) = h4/pred__set/INSERT e (h4/bag/SET__OF__BAG b)
% Goal: !e. h4/bag/SET__OF__BAG (h4/bag/EL__BAG e) = h4/pred__set/INSERT e 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_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_bags_ELu_u_BAG0]: !e. h4/bag/EL__BAG e = h4/bag/BAG__INSERT e h4/bag/EMPTY__BAG
% Assm [h4s_bags_BAGu_u_OFu_u_EMPTY]: h4/bag/SET__OF__BAG h4/bag/EMPTY__BAG = h4/pred__set/EMPTY
% Assm [h4s_bags_SETu_u_OFu_u_BAGu_u_INSERT]: !e b. h4/bag/SET__OF__BAG (h4/bag/BAG__INSERT e b) = h4/pred__set/INSERT e (h4/bag/SET__OF__BAG b)
% Goal: !e. h4/bag/SET__OF__BAG (h4/bag/EL__BAG e) = h4/pred__set/INSERT e 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_Q230108,TV_Q230104]: ![V_f, V_g]: (![V_x]: s(TV_Q230104,happ(s(t_fun(TV_Q230108,TV_Q230104),V_f),s(TV_Q230108,V_x))) = s(TV_Q230104,happ(s(t_fun(TV_Q230108,TV_Q230104),V_g),s(TV_Q230108,V_x))) => s(t_fun(TV_Q230108,TV_Q230104),V_f) = s(t_fun(TV_Q230108,TV_Q230104),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_bags_ELu_u_BAG0, axiom, ![TV_u_27a]: ![V_e]: s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_elu_u_bag(s(TV_u_27a,V_e))) = s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(TV_u_27a,V_e),s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_emptyu_u_bag)))).
fof(ah4s_bags_BAGu_u_OFu_u_EMPTY, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_bool),h4s_bags_setu_u_ofu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_emptyu_u_bag))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)).
fof(ah4s_bags_SETu_u_OFu_u_BAGu_u_INSERT, axiom, ![TV_u_27a]: ![V_e, V_b]: s(t_fun(TV_u_27a,t_bool),h4s_bags_setu_u_ofu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(TV_u_27a,V_e),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b))))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_e),s(t_fun(TV_u_27a,t_bool),h4s_bags_setu_u_ofu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b)))))).
fof(ch4s_bags_SETu_u_OFu_u_ELu_u_BAG, conjecture, ![TV_u_27a]: ![V_e]: s(t_fun(TV_u_27a,t_bool),h4s_bags_setu_u_ofu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_elu_u_bag(s(TV_u_27a,V_e))))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_e),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))).
