%   ORIGINAL: h4/bool/itself__Axiom
% 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: !e. ?f. f h4/bool/the__value = 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
% Goal: !e. ?f. happ f h4/bool/the__value = e
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q294215,TV_Q294211]: ![V_f, V_g]: (![V_x]: s(TV_Q294211,happ(s(t_fun(TV_Q294215,TV_Q294211),V_f),s(TV_Q294215,V_x))) = s(TV_Q294211,happ(s(t_fun(TV_Q294215,TV_Q294211),V_g),s(TV_Q294215,V_x))) => s(t_fun(TV_Q294215,TV_Q294211),V_f) = s(t_fun(TV_Q294215,TV_Q294211),V_g))).
fof(ch4s_bools_itselfu_u_Axiom, conjecture, ![TV_u_27b,TV_u_27a]: ![V_e]: ?[V_f]: s(TV_u_27a,happ(s(t_fun(t_h4s_bools_itself(TV_u_27b),TV_u_27a),V_f),s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))) = s(TV_u_27a,V_e)).
