%   ORIGINAL: h4/bag/SUB__BAG__DIFF__simple
% 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_c3: !t. t ==> t <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> 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/SUB__BAG__DIFF_c0: !b2 b1. h4/bag/SUB__BAG b1 b2 ==> (!b3. h4/bag/SUB__BAG (h4/bag/BAG__DIFF b1 b3) b2)
% Goal: !c b. h4/bag/SUB__BAG (h4/bag/BAG__DIFF b c) b
%   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_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> 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_SUBu_u_BAGu_u_DIFFu_c0]: !b2 b1. h4/bag/SUB__BAG b1 b2 ==> (!b3. h4/bag/SUB__BAG (h4/bag/BAG__DIFF b1 b3) b2)
% Goal: !c b. h4/bag/SUB__BAG (h4/bag/BAG__DIFF b c) b
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_Q233638,TV_Q233634]: ![V_f, V_g]: (![V_x]: s(TV_Q233634,happ(s(t_fun(TV_Q233638,TV_Q233634),V_f),s(TV_Q233638,V_x))) = s(TV_Q233634,happ(s(t_fun(TV_Q233638,TV_Q233634),V_g),s(TV_Q233638,V_x))) => s(t_fun(TV_Q233638,TV_Q233634),V_f) = s(t_fun(TV_Q233638,TV_Q233634),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_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_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_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_SUBu_u_BAGu_u_DIFFu_c0, 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_b3]: p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_diff(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b1),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b3))),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b2)))))).
fof(ch4s_bags_SUBu_u_BAGu_u_DIFFu_u_simple, conjecture, ![TV_u_27a]: ![V_c, V_b]: p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_diff(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b),s(t_fun(TV_u_27a,t_h4s_nums_num),V_c))),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b))))).
