%   ORIGINAL: h4/realax/real__ABS__REP__CLASS_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/realax/real__bijections_c0: !a. h4/realax/real__ABS__CLASS (h4/realax/real__REP__CLASS a) = a
% Assm: h4/realax/real__bijections_c1: !r. (\c. ?r0. h4/realax/treal__eq r0 r0 /\ c = h4/realax/treal__eq r0) r <=> h4/realax/real__REP__CLASS (h4/realax/real__ABS__CLASS r) = r
% Goal: !a. h4/realax/real__ABS__CLASS (h4/realax/real__REP__CLASS 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_realaxs_realu_u_bijectionsu_c0]: !a. h4/realax/real__ABS__CLASS (h4/realax/real__REP__CLASS a) = a
% Assm [h4s_realaxs_realu_u_bijectionsu_c1]: !r. (?r0. happ (h4/realax/treal__eq r0) r0 /\ r = h4/realax/treal__eq r0) <=> h4/realax/real__REP__CLASS (h4/realax/real__ABS__CLASS r) = r
% Goal: !a. h4/realax/real__ABS__CLASS (h4/realax/real__REP__CLASS 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_Q329242,TV_Q329238]: ![V_f, V_g]: (![V_x]: s(TV_Q329238,happ(s(t_fun(TV_Q329242,TV_Q329238),V_f),s(TV_Q329242,V_x))) = s(TV_Q329238,happ(s(t_fun(TV_Q329242,TV_Q329238),V_g),s(TV_Q329242,V_x))) => s(t_fun(TV_Q329242,TV_Q329238),V_f) = s(t_fun(TV_Q329242,TV_Q329238),V_g))).
fof(ah4s_realaxs_realu_u_bijectionsu_c0, axiom, ![V_a]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_absu_u_class(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),h4s_realaxs_realu_u_repu_u_class(s(t_h4s_realaxs_real,V_a))))) = s(t_h4s_realaxs_real,V_a)).
fof(ah4s_realaxs_realu_u_bijectionsu_c1, axiom, ![V_r]: (?[V_r0]: (p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),h4s_realaxs_trealu_u_eq(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_r0))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_r0)))) & s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),V_r) = s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),h4s_realaxs_trealu_u_eq(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),V_r0)))) <=> s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),h4s_realaxs_realu_u_repu_u_class(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_absu_u_class(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),V_r))))) = s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),V_r))).
fof(ch4s_realaxs_realu_u_ABSu_u_REPu_u_CLASSu_c0, conjecture, ![V_a]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_absu_u_class(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),h4s_realaxs_realu_u_repu_u_class(s(t_h4s_realaxs_real,V_a))))) = s(t_h4s_realaxs_real,V_a)).
