%   ORIGINAL: h4/toto/datatype__num__dt
% 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/DATATYPE__TAG__THM: !x. h4/bool/DATATYPE x <=> T
% Goal: !num__dt. h4/bool/DATATYPE (num__dt h4/toto/zer h4/toto/bit1 h4/toto/bit2)
%   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_DATATYPEu_u_TAGu_u_THM]: !x. h4/bool/DATATYPE x <=> T
% Goal: !num__dt. h4/bool/DATATYPE (happ (happ (happ num__dt h4/toto/zer) h4/toto/bit1) h4/toto/bit2)
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_Q251907,TV_Q251903]: ![V_f, V_g]: (![V_x]: s(TV_Q251903,happ(s(t_fun(TV_Q251907,TV_Q251903),V_f),s(TV_Q251907,V_x))) = s(TV_Q251903,happ(s(t_fun(TV_Q251907,TV_Q251903),V_g),s(TV_Q251907,V_x))) => s(t_fun(TV_Q251907,TV_Q251903),V_f) = s(t_fun(TV_Q251907,TV_Q251903),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_DATATYPEu_u_TAGu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_datatype(s(TV_u_27a,V_x))) = s(t_bool,t)).
fof(ch4s_totos_datatypeu_u_numu_u_dt, conjecture, ![V_numu_u_dt]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_bool),happ(s(t_fun(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_fun(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_bool)),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_fun(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_bool))),V_numu_u_dt),s(t_h4s_totos_numu_u_dt,h4s_totos_zer))),s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1))),s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2))))))).
