%   ORIGINAL: h4/prelim/num2ordering__thm_c0
% 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/prelim/LESS__def: h4/prelim/LESS = h4/prelim/num2ordering h4/num/0
% Goal: h4/prelim/num2ordering h4/num/0 = h4/prelim/LESS
%   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_prelims_LESSu_u_def]: h4/prelim/LESS = h4/prelim/num2ordering h4/num/0
% Goal: h4/prelim/num2ordering h4/num/0 = h4/prelim/LESS
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_Q188420,TV_Q188416]: ![V_f, V_g]: (![V_x]: s(TV_Q188416,happ(s(t_fun(TV_Q188420,TV_Q188416),V_f),s(TV_Q188420,V_x))) = s(TV_Q188416,happ(s(t_fun(TV_Q188420,TV_Q188416),V_g),s(TV_Q188420,V_x))) => s(t_fun(TV_Q188420,TV_Q188416),V_f) = s(t_fun(TV_Q188420,TV_Q188416),V_g))).
fof(ah4s_prelims_LESSu_u_def, axiom, s(t_h4s_prelims_ordering,h4s_prelims_less) = s(t_h4s_prelims_ordering,h4s_prelims_num2ordering(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ch4s_prelims_num2orderingu_u_thmu_c0, conjecture, s(t_h4s_prelims_ordering,h4s_prelims_num2ordering(s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_prelims_ordering,h4s_prelims_less)).
