%   ORIGINAL: h4/prelim/datatype__ordering
% 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: !ordering. h4/bool/DATATYPE (ordering h4/prelim/LESS h4/prelim/EQUAL h4/prelim/GREATER)
%   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: !ordering. h4/bool/DATATYPE (happ (happ (happ ordering h4/prelim/LESS) h4/prelim/EQUAL) h4/prelim/GREATER)
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_Q188673,TV_Q188669]: ![V_f, V_g]: (![V_x]: s(TV_Q188669,happ(s(t_fun(TV_Q188673,TV_Q188669),V_f),s(TV_Q188673,V_x))) = s(TV_Q188669,happ(s(t_fun(TV_Q188673,TV_Q188669),V_g),s(TV_Q188673,V_x))) => s(t_fun(TV_Q188673,TV_Q188669),V_f) = s(t_fun(TV_Q188673,TV_Q188669),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_prelims_datatypeu_u_ordering, conjecture, ![V_ordering]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_h4s_prelims_ordering,t_bool),happ(s(t_fun(t_h4s_prelims_ordering,t_fun(t_h4s_prelims_ordering,t_bool)),happ(s(t_fun(t_h4s_prelims_ordering,t_fun(t_h4s_prelims_ordering,t_fun(t_h4s_prelims_ordering,t_bool))),V_ordering),s(t_h4s_prelims_ordering,h4s_prelims_less))),s(t_h4s_prelims_ordering,h4s_prelims_equal))),s(t_h4s_prelims_ordering,h4s_prelims_greater))))))).
