%   ORIGINAL: h4/bag/SUB__BAG__SET
% 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/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/pred__set/SPECIFICATION: !x P. h4/bool/IN x P <=> P x
% Assm: h4/pred__set/SUBSET__DEF: !t s. h4/pred__set/SUBSET s t <=> (!x. h4/bool/IN x s ==> h4/bool/IN x t)
% Assm: h4/bag/SUB__BAG0: !b2 b1. h4/bag/SUB__BAG b1 b2 <=> (!x n. h4/bag/BAG__INN x n b1 ==> h4/bag/BAG__INN x n b2)
% Assm: h4/bag/BAG__IN0: !e b. h4/bag/BAG__IN e b <=> h4/bag/BAG__INN e (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b
% Assm: h4/bag/SET__OF__BAG0: !b. h4/bag/SET__OF__BAG b = (\x. h4/bag/BAG__IN x b)
% Goal: !b2 b1. h4/bag/SUB__BAG b1 b2 ==> h4/pred__set/SUBSET (h4/bag/SET__OF__BAG b1) (h4/bag/SET__OF__BAG b2)
%   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_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_predu_u_sets_SPECIFICATION]: !x P. h4/bool/IN x P <=> happ P x
% Assm [h4s_predu_u_sets_SUBSETu_u_DEF]: !t s. h4/pred__set/SUBSET s t <=> (!x. h4/bool/IN x s ==> h4/bool/IN x t)
% Assm [h4s_bags_SUBu_u_BAG0]: !b2 b1. h4/bag/SUB__BAG b1 b2 <=> (!x n. h4/bag/BAG__INN x n b1 ==> h4/bag/BAG__INN x n b2)
% Assm [h4s_bags_BAGu_u_IN0]: !e b. h4/bag/BAG__IN e b <=> h4/bag/BAG__INN e (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b
% Assm [h4s_bags_SETu_u_OFu_u_BAG0]: !b x. happ (h4/bag/SET__OF__BAG b) x <=> h4/bag/BAG__IN x b
% Goal: !b2 b1. h4/bag/SUB__BAG b1 b2 ==> h4/pred__set/SUBSET (h4/bag/SET__OF__BAG b1) (h4/bag/SET__OF__BAG b2)
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_Q230006,TV_Q230002]: ![V_f, V_g]: (![V_x]: s(TV_Q230002,happ(s(t_fun(TV_Q230006,TV_Q230002),V_f),s(TV_Q230006,V_x))) = s(TV_Q230002,happ(s(t_fun(TV_Q230006,TV_Q230002),V_g),s(TV_Q230006,V_x))) => s(t_fun(TV_Q230006,TV_Q230002),V_f) = s(t_fun(TV_Q230006,TV_Q230002),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_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> 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_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_predu_u_sets_SPECIFICATION, axiom, ![TV_u_27a]: ![V_x, V_P]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_P))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))).
fof(ah4s_predu_u_sets_SUBSETu_u_DEF, axiom, ![TV_u_27a]: ![V_t, V_s]: (p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))) <=> ![V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) => p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))))).
fof(ah4s_bags_SUBu_u_BAG0, axiom, ![TV_u_27a]: ![V_b2, V_b1]: (p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b1),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b2)))) <=> ![V_x, V_n]: (p(s(t_bool,h4s_bags_bagu_u_inn(s(TV_u_27a,V_x),s(t_h4s_nums_num,V_n),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b1)))) => p(s(t_bool,h4s_bags_bagu_u_inn(s(TV_u_27a,V_x),s(t_h4s_nums_num,V_n),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b2))))))).
fof(ah4s_bags_BAGu_u_IN0, axiom, ![TV_u_27a]: ![V_e, V_b]: s(t_bool,h4s_bags_bagu_u_in(s(TV_u_27a,V_e),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b))) = s(t_bool,h4s_bags_bagu_u_inn(s(TV_u_27a,V_e),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b)))).
fof(ah4s_bags_SETu_u_OFu_u_BAG0, axiom, ![TV_u_27a]: ![V_b, V_x]: s(t_bool,happ(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))),s(TV_u_27a,V_x))) = s(t_bool,h4s_bags_bagu_u_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b)))).
fof(ch4s_bags_SUBu_u_BAGu_u_SET, conjecture, ![TV_u_27a]: ![V_b2, V_b1]: (p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b1),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b2)))) => p(s(t_bool,h4s_predu_u_sets_subset(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_b1))),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_b2)))))))).
