%   ORIGINAL: h4/prelim/ordering2num__11
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/prelim/ordering__BIJ_c0: !a. h4/prelim/num2ordering (h4/prelim/ordering2num a) = a
% Goal: !a_27 a. h4/prelim/ordering2num a = h4/prelim/ordering2num a_27 <=> a = a_27
%   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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_prelims_orderingu_u_BIJu_c0]: !a. h4/prelim/num2ordering (h4/prelim/ordering2num a) = a
% Goal: !a_27 a. h4/prelim/ordering2num a = h4/prelim/ordering2num a_27 <=> a = a_27
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_Q188345,TV_Q188341]: ![V_f, V_g]: (![V_x]: s(TV_Q188341,happ(s(t_fun(TV_Q188345,TV_Q188341),V_f),s(TV_Q188345,V_x))) = s(TV_Q188341,happ(s(t_fun(TV_Q188345,TV_Q188341),V_g),s(TV_Q188345,V_x))) => s(t_fun(TV_Q188345,TV_Q188341),V_f) = s(t_fun(TV_Q188345,TV_Q188341),V_g))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_prelims_orderingu_u_BIJu_c0, axiom, ![V_a]: s(t_h4s_prelims_ordering,h4s_prelims_num2ordering(s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,V_a))))) = s(t_h4s_prelims_ordering,V_a)).
fof(ch4s_prelims_ordering2numu_u_11, conjecture, ![V_au_27, V_a]: (s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,V_a))) = s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,V_au_27))) <=> s(t_h4s_prelims_ordering,V_a) = s(t_h4s_prelims_ordering,V_au_27))).
