%   ORIGINAL: h4/measure/BOREL__MEASURABLE__SETS_c8
% 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/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/measure/BOREL__MEASURABLE__SETS9: !c. h4/bool/IN (h4/pred__set/INSERT c h4/pred__set/EMPTY) (h4/measure/subsets h4/measure/Borel)
% Goal: !c. h4/bool/IN (h4/pred__set/INSERT c h4/pred__set/EMPTY) (h4/measure/subsets h4/measure/Borel)
%   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_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_measures_BORELu_u_MEASURABLEu_u_SETS9]: !c. h4/bool/IN (h4/pred__set/INSERT c h4/pred__set/EMPTY) (h4/measure/subsets h4/measure/Borel)
% Goal: !c. h4/bool/IN (h4/pred__set/INSERT c h4/pred__set/EMPTY) (h4/measure/subsets h4/measure/Borel)
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_Q114777,TV_Q114773]: ![V_f, V_g]: (![V_x]: s(TV_Q114773,happ(s(t_fun(TV_Q114777,TV_Q114773),V_f),s(TV_Q114777,V_x))) = s(TV_Q114773,happ(s(t_fun(TV_Q114777,TV_Q114773),V_g),s(TV_Q114777,V_x))) => s(t_fun(TV_Q114777,TV_Q114773),V_f) = s(t_fun(TV_Q114777,TV_Q114773),V_g))).
fof(ah4s_bools_TRUTH, axiom, 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_measures_BORELu_u_MEASURABLEu_u_SETS9, axiom, ![V_c]: p(s(t_bool,h4s_bools_in(s(t_fun(t_h4s_extreals_extreal,t_bool),h4s_predu_u_sets_insert(s(t_h4s_extreals_extreal,V_c),s(t_fun(t_h4s_extreals_extreal,t_bool),h4s_predu_u_sets_empty))),s(t_fun(t_fun(t_h4s_extreals_extreal,t_bool),t_bool),h4s_measures_subsets(s(t_h4s_pairs_prod(t_fun(t_h4s_extreals_extreal,t_bool),t_fun(t_fun(t_h4s_extreals_extreal,t_bool),t_bool)),h4s_measures_borel))))))).
fof(ch4s_measures_BORELu_u_MEASURABLEu_u_SETSu_c8, conjecture, ![V_c]: p(s(t_bool,h4s_bools_in(s(t_fun(t_h4s_extreals_extreal,t_bool),h4s_predu_u_sets_insert(s(t_h4s_extreals_extreal,V_c),s(t_fun(t_h4s_extreals_extreal,t_bool),h4s_predu_u_sets_empty))),s(t_fun(t_fun(t_h4s_extreals_extreal,t_bool),t_bool),h4s_measures_subsets(s(t_h4s_pairs_prod(t_fun(t_h4s_extreals_extreal,t_bool),t_fun(t_fun(t_h4s_extreals_extreal,t_bool),t_bool)),h4s_measures_borel))))))).
