%   ORIGINAL: h4/bag/BAG__GEN__SUM__EMPTY
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bag/ITBAG__EMPTY: !f acc. h4/bag/ITBAG f h4/bag/EMPTY__BAG acc = acc
% Assm: h4/bag/BAG__GEN__SUM__def: !n bag. h4/bag/BAG__GEN__SUM bag n = h4/bag/ITBAG h4/arithmetic/_2B bag n
% Goal: !n. h4/bag/BAG__GEN__SUM h4/bag/EMPTY__BAG n = n
%   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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bags_ITBAGu_u_EMPTY]: !f acc. h4/bag/ITBAG f h4/bag/EMPTY__BAG acc = acc
% Assm [h4s_bags_BAGu_u_GENu_u_SUMu_u_def]: !n bag. h4/bag/BAG__GEN__SUM bag n = h4/bag/ITBAG h4/arithmetic/_2B bag n
% Goal: !n. h4/bag/BAG__GEN__SUM h4/bag/EMPTY__BAG n = n
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_Q231797,TV_Q231793]: ![V_f, V_g]: (![V_x]: s(TV_Q231793,happ(s(t_fun(TV_Q231797,TV_Q231793),V_f),s(TV_Q231797,V_x))) = s(TV_Q231793,happ(s(t_fun(TV_Q231797,TV_Q231793),V_g),s(TV_Q231797,V_x))) => s(t_fun(TV_Q231797,TV_Q231793),V_f) = s(t_fun(TV_Q231797,TV_Q231793),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bags_ITBAGu_u_EMPTY, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_acc]: s(TV_u_27b,h4s_bags_itbag(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_emptyu_u_bag),s(TV_u_27b,V_acc))) = s(TV_u_27b,V_acc)).
fof(ah4s_bags_BAGu_u_GENu_u_SUMu_u_def, axiom, ![V_n, V_bag]: s(t_h4s_nums_num,h4s_bags_bagu_u_genu_u_sum(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),V_bag),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_bags_itbag(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),V_bag),s(t_h4s_nums_num,V_n)))).
fof(ch4s_bags_BAGu_u_GENu_u_SUMu_u_EMPTY, conjecture, ![V_n]: s(t_h4s_nums_num,h4s_bags_bagu_u_genu_u_sum(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_bags_emptyu_u_bag),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,V_n)).
