%   ORIGINAL: h4/bag/BAG__DELETE__BAG__IN__up
% 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/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bag/BAG__IN__BAG__INSERT: !e2 e1 b. h4/bag/BAG__IN e1 (h4/bag/BAG__INSERT e2 b) <=> e1 = e2 \/ h4/bag/BAG__IN e1 b
% Assm: h4/bag/BAG__DELETE0: !e b0 b. h4/bag/BAG__DELETE b0 e b <=> b0 = h4/bag/BAG__INSERT e b
% Goal: !e b0 b. h4/bag/BAG__DELETE b0 e b ==> (!e_27. h4/bag/BAG__IN e_27 b ==> h4/bag/BAG__IN e_27 b0)
%   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_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bags_BAGu_u_INu_u_BAGu_u_INSERT]: !e2 e1 b. h4/bag/BAG__IN e1 (h4/bag/BAG__INSERT e2 b) <=> e1 = e2 \/ h4/bag/BAG__IN e1 b
% Assm [h4s_bags_BAGu_u_DELETE0]: !e b0 b. h4/bag/BAG__DELETE b0 e b <=> b0 = h4/bag/BAG__INSERT e b
% Goal: !e b0 b. h4/bag/BAG__DELETE b0 e b ==> (!e_27. h4/bag/BAG__IN e_27 b ==> h4/bag/BAG__IN e_27 b0)
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_Q227619,TV_Q227615]: ![V_f, V_g]: (![V_x]: s(TV_Q227615,happ(s(t_fun(TV_Q227619,TV_Q227615),V_f),s(TV_Q227619,V_x))) = s(TV_Q227615,happ(s(t_fun(TV_Q227619,TV_Q227615),V_g),s(TV_Q227619,V_x))) => s(t_fun(TV_Q227619,TV_Q227615),V_f) = s(t_fun(TV_Q227619,TV_Q227615),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ORu_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_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bags_BAGu_u_INu_u_BAGu_u_INSERT, axiom, ![TV_u_27a]: ![V_e2, V_e1, V_b]: (p(s(t_bool,h4s_bags_bagu_u_in(s(TV_u_27a,V_e1),s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(TV_u_27a,V_e2),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b)))))) <=> (s(TV_u_27a,V_e1) = s(TV_u_27a,V_e2) | p(s(t_bool,h4s_bags_bagu_u_in(s(TV_u_27a,V_e1),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b))))))).
fof(ah4s_bags_BAGu_u_DELETE0, axiom, ![TV_u_27a]: ![V_e, V_b0, V_b]: (p(s(t_bool,h4s_bags_bagu_u_delete(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b0),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_h4s_nums_num),V_b0) = 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))))).
fof(ch4s_bags_BAGu_u_DELETEu_u_BAGu_u_INu_u_up, conjecture, ![TV_u_27a]: ![V_e, V_b0, V_b]: (p(s(t_bool,h4s_bags_bagu_u_delete(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b0),s(TV_u_27a,V_e),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b)))) => ![V_eu_27]: (p(s(t_bool,h4s_bags_bagu_u_in(s(TV_u_27a,V_eu_27),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b)))) => p(s(t_bool,h4s_bags_bagu_u_in(s(TV_u_27a,V_eu_27),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b0))))))).
