%   ORIGINAL: h4/realax/SUP__ALLPOS__LEMMA2
% 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
% Goal: !X P. P (h4/realax/real__of__hreal X) <=> (\h. P (h4/realax/real__of__hreal h)) X
%   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
% Goal: !X P. happ P (h4/realax/real__of__hreal X) <=> happ P (h4/realax/real__of__hreal X)
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_Q329392,TV_Q329388]: ![V_f, V_g]: (![V_x]: s(TV_Q329388,happ(s(t_fun(TV_Q329392,TV_Q329388),V_f),s(TV_Q329392,V_x))) = s(TV_Q329388,happ(s(t_fun(TV_Q329392,TV_Q329388),V_g),s(TV_Q329392,V_x))) => s(t_fun(TV_Q329392,TV_Q329388),V_f) = s(t_fun(TV_Q329392,TV_Q329388),V_g))).
fof(ch4s_realaxs_SUPu_u_ALLPOSu_u_LEMMA2, conjecture, ![V_X, V_P]: s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),V_P),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_ofu_u_hreal(s(t_h4s_hreals_hreal,V_X))))) = s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),V_P),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_ofu_u_hreal(s(t_h4s_hreals_hreal,V_X)))))).
