%   ORIGINAL: h4/bool/DATATYPE__BOOL
% 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/DATATYPE__TAG__DEF: h4/bool/DATATYPE = (\x. T)
% Goal: !bool. h4/bool/DATATYPE (bool T F) <=> T
%   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_DATATYPEu_u_TAGu_u_DEF]: !x. h4/bool/DATATYPE x <=> T
% Goal: !bool. h4/bool/DATATYPE (happ (happ bool T) F) <=> T
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_Q294165,TV_Q294161]: ![V_f, V_g]: (![V_x]: s(TV_Q294161,happ(s(t_fun(TV_Q294165,TV_Q294161),V_f),s(TV_Q294165,V_x))) = s(TV_Q294161,happ(s(t_fun(TV_Q294165,TV_Q294161),V_g),s(TV_Q294165,V_x))) => s(t_fun(TV_Q294165,TV_Q294161),V_f) = s(t_fun(TV_Q294165,TV_Q294161),V_g))).
fof(ah4s_bools_DATATYPEu_u_TAGu_u_DEF, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_datatype(s(TV_u_27a,V_x))) = s(t_bool,t)).
fof(ch4s_bools_DATATYPEu_u_BOOL, conjecture, ![V_bool]: s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_bool),s(t_bool,t))),s(t_bool,f))))) = s(t_bool,t)).
