%   ORIGINAL: h4/pred__set/MAX__SET__REWRITES_c1
% 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/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/arithmetic/MAX__0_c0: !n. h4/arithmetic/MAX n h4/num/0 = n
% Assm: h4/pred__set/FINITE__EMPTY: h4/pred__set/FINITE h4/pred__set/EMPTY
% Assm: h4/pred__set/MAX__SET__THM_c0: h4/pred__set/MAX__SET h4/pred__set/EMPTY = h4/num/0
% Assm: h4/pred__set/MAX__SET__THM_c1: !s e. h4/pred__set/FINITE s ==> h4/pred__set/MAX__SET (h4/pred__set/INSERT e s) = h4/arithmetic/MAX e (h4/pred__set/MAX__SET s)
% Goal: !e. h4/pred__set/MAX__SET (h4/pred__set/INSERT e h4/pred__set/EMPTY) = e
%   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_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_arithmetics_MAXu_u_0u_c0]: !n. h4/arithmetic/MAX n h4/num/0 = n
% Assm [h4s_predu_u_sets_FINITEu_u_EMPTY]: h4/pred__set/FINITE h4/pred__set/EMPTY
% Assm [h4s_predu_u_sets_MAXu_u_SETu_u_THMu_c0]: h4/pred__set/MAX__SET h4/pred__set/EMPTY = h4/num/0
% Assm [h4s_predu_u_sets_MAXu_u_SETu_u_THMu_c1]: !s e. h4/pred__set/FINITE s ==> h4/pred__set/MAX__SET (h4/pred__set/INSERT e s) = h4/arithmetic/MAX e (h4/pred__set/MAX__SET s)
% Goal: !e. h4/pred__set/MAX__SET (h4/pred__set/INSERT e h4/pred__set/EMPTY) = e
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_Q154909,TV_Q154905]: ![V_f, V_g]: (![V_x]: s(TV_Q154905,happ(s(t_fun(TV_Q154909,TV_Q154905),V_f),s(TV_Q154909,V_x))) = s(TV_Q154905,happ(s(t_fun(TV_Q154909,TV_Q154905),V_g),s(TV_Q154909,V_x))) => s(t_fun(TV_Q154909,TV_Q154905),V_f) = s(t_fun(TV_Q154909,TV_Q154905),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_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_arithmetics_MAXu_u_0u_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_max(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_predu_u_sets_FINITEu_u_EMPTY, axiom, ![TV_u_27a]: p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))))).
fof(ah4s_predu_u_sets_MAXu_u_SETu_u_THMu_c0, axiom, s(t_h4s_nums_num,h4s_predu_u_sets_maxu_u_set(s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_predu_u_sets_MAXu_u_SETu_u_THMu_c1, axiom, ![V_s, V_e]: (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),V_s)))) => s(t_h4s_nums_num,h4s_predu_u_sets_maxu_u_set(s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_insert(s(t_h4s_nums_num,V_e),s(t_fun(t_h4s_nums_num,t_bool),V_s))))) = s(t_h4s_nums_num,h4s_arithmetics_max(s(t_h4s_nums_num,V_e),s(t_h4s_nums_num,h4s_predu_u_sets_maxu_u_set(s(t_fun(t_h4s_nums_num,t_bool),V_s))))))).
fof(ch4s_predu_u_sets_MAXu_u_SETu_u_REWRITESu_c1, conjecture, ![V_e]: s(t_h4s_nums_num,h4s_predu_u_sets_maxu_u_set(s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_insert(s(t_h4s_nums_num,V_e),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty))))) = s(t_h4s_nums_num,V_e)).
