%   ORIGINAL: h4/bag/mlt__UNION__LCANCEL
% 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/bag/COMM__BAG__UNION: !b2 b1. h4/bag/BAG__UNION b1 b2 = h4/bag/BAG__UNION b2 b1
% Assm: h4/bag/mlt__UNION__RCANCEL: !c b a R. h4/relation/WF R /\ h4/relation/transitive R ==> (h4/relation/TC (h4/bag/mlt1 R) (h4/bag/BAG__UNION a c) (h4/bag/BAG__UNION b c) <=> h4/relation/TC (h4/bag/mlt1 R) a b /\ h4/bag/FINITE__BAG c)
% Goal: !c b a R. h4/relation/WF R /\ h4/relation/transitive R ==> (h4/relation/TC (h4/bag/mlt1 R) (h4/bag/BAG__UNION c a) (h4/bag/BAG__UNION c b) <=> h4/relation/TC (h4/bag/mlt1 R) a b /\ h4/bag/FINITE__BAG c)
%   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_bags_COMMu_u_BAGu_u_UNION]: !b2 b1. h4/bag/BAG__UNION b1 b2 = h4/bag/BAG__UNION b2 b1
% Assm [h4s_bags_mltu_u_UNIONu_u_RCANCEL]: !c b a R. h4/relation/WF R /\ h4/relation/transitive R ==> (h4/relation/TC (h4/bag/mlt1 R) (h4/bag/BAG__UNION a c) (h4/bag/BAG__UNION b c) <=> h4/relation/TC (h4/bag/mlt1 R) a b /\ h4/bag/FINITE__BAG c)
% Goal: !c b a R. h4/relation/WF R /\ h4/relation/transitive R ==> (h4/relation/TC (h4/bag/mlt1 R) (h4/bag/BAG__UNION c a) (h4/bag/BAG__UNION c b) <=> h4/relation/TC (h4/bag/mlt1 R) a b /\ h4/bag/FINITE__BAG c)
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_Q233537,TV_Q233533]: ![V_f, V_g]: (![V_x]: s(TV_Q233533,happ(s(t_fun(TV_Q233537,TV_Q233533),V_f),s(TV_Q233537,V_x))) = s(TV_Q233533,happ(s(t_fun(TV_Q233537,TV_Q233533),V_g),s(TV_Q233537,V_x))) => s(t_fun(TV_Q233537,TV_Q233533),V_f) = s(t_fun(TV_Q233537,TV_Q233533),V_g))).
fof(ah4s_bags_COMMu_u_BAGu_u_UNION, axiom, ![TV_u_27a]: ![V_b2, V_b1]: s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b1),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b2))) = s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b2),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b1)))).
fof(ah4s_bags_mltu_u_UNIONu_u_RCANCEL, axiom, ![TV_u_27a]: ![V_c, V_b, V_a, V_R]: ((p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) & p(s(t_bool,h4s_relations_transitive(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))))) => (p(s(t_bool,h4s_relations_tc(s(t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_bool)),h4s_bags_mlt1(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(TV_u_27a,t_h4s_nums_num),V_a),s(t_fun(TV_u_27a,t_h4s_nums_num),V_c))),s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b),s(t_fun(TV_u_27a,t_h4s_nums_num),V_c)))))) <=> (p(s(t_bool,h4s_relations_tc(s(t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_bool)),h4s_bags_mlt1(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),s(t_fun(TV_u_27a,t_h4s_nums_num),V_a),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b)))) & p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),V_c)))))))).
fof(ch4s_bags_mltu_u_UNIONu_u_LCANCEL, conjecture, ![TV_u_27a]: ![V_c, V_b, V_a, V_R]: ((p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) & p(s(t_bool,h4s_relations_transitive(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))))) => (p(s(t_bool,h4s_relations_tc(s(t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_bool)),h4s_bags_mlt1(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(TV_u_27a,t_h4s_nums_num),V_c),s(t_fun(TV_u_27a,t_h4s_nums_num),V_a))),s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(TV_u_27a,t_h4s_nums_num),V_c),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b)))))) <=> (p(s(t_bool,h4s_relations_tc(s(t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_bool)),h4s_bags_mlt1(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),s(t_fun(TV_u_27a,t_h4s_nums_num),V_a),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b)))) & p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),V_c)))))))).
