%   ORIGINAL: h4/pred__set/INTER__UNION_c0
% 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/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/pred__set/SUBSET__UNION_c0: !t s. h4/pred__set/SUBSET s (h4/pred__set/UNION s t)
% Assm: h4/pred__set/SUBSET__UNION_c1: !t s. h4/pred__set/SUBSET s (h4/pred__set/UNION t s)
% Assm: h4/pred__set/INTER__SUBSET__EQN_c0: !B A. h4/pred__set/INTER A B = A <=> h4/pred__set/SUBSET A B
% Assm: h4/pred__set/INTER__SUBSET__EQN_c1: !B A. h4/pred__set/INTER A B = B <=> h4/pred__set/SUBSET B A
% Goal: !B A. h4/pred__set/INTER (h4/pred__set/UNION A B) A = A
%   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_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_predu_u_sets_SUBSETu_u_UNIONu_c0]: !t s. h4/pred__set/SUBSET s (h4/pred__set/UNION s t)
% Assm [h4s_predu_u_sets_SUBSETu_u_UNIONu_c1]: !t s. h4/pred__set/SUBSET s (h4/pred__set/UNION t s)
% Assm [h4s_predu_u_sets_INTERu_u_SUBSETu_u_EQNu_c0]: !B A. h4/pred__set/INTER A B = A <=> h4/pred__set/SUBSET A B
% Assm [h4s_predu_u_sets_INTERu_u_SUBSETu_u_EQNu_c1]: !B A. h4/pred__set/INTER A B = B <=> h4/pred__set/SUBSET B A
% Goal: !B A. h4/pred__set/INTER (h4/pred__set/UNION A B) A = A
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_Q157030,TV_Q157026]: ![V_f, V_g]: (![V_x]: s(TV_Q157026,happ(s(t_fun(TV_Q157030,TV_Q157026),V_f),s(TV_Q157030,V_x))) = s(TV_Q157026,happ(s(t_fun(TV_Q157030,TV_Q157026),V_g),s(TV_Q157030,V_x))) => s(t_fun(TV_Q157030,TV_Q157026),V_f) = s(t_fun(TV_Q157030,TV_Q157026),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_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_predu_u_sets_SUBSETu_u_UNIONu_c0, 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),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t))))))).
fof(ah4s_predu_u_sets_SUBSETu_u_UNIONu_c1, 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),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_t),s(t_fun(TV_u_27a,t_bool),V_s))))))).
fof(ah4s_predu_u_sets_INTERu_u_SUBSETu_u_EQNu_c0, axiom, ![TV_u_27a]: ![V_B, V_A]: (s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_inter(s(t_fun(TV_u_27a,t_bool),V_A),s(t_fun(TV_u_27a,t_bool),V_B))) = s(t_fun(TV_u_27a,t_bool),V_A) <=> p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_A),s(t_fun(TV_u_27a,t_bool),V_B)))))).
fof(ah4s_predu_u_sets_INTERu_u_SUBSETu_u_EQNu_c1, axiom, ![TV_u_27a]: ![V_B, V_A]: (s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_inter(s(t_fun(TV_u_27a,t_bool),V_A),s(t_fun(TV_u_27a,t_bool),V_B))) = s(t_fun(TV_u_27a,t_bool),V_B) <=> p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_B),s(t_fun(TV_u_27a,t_bool),V_A)))))).
fof(ch4s_predu_u_sets_INTERu_u_UNIONu_c0, conjecture, ![TV_u_27a]: ![V_B, V_A]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_inter(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_A),s(t_fun(TV_u_27a,t_bool),V_B))),s(t_fun(TV_u_27a,t_bool),V_A))) = s(t_fun(TV_u_27a,t_bool),V_A)).
