%   ORIGINAL: h4/ieee/num2roundmode__thm_c1
% 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/ieee/float__To__zero__def: h4/ieee/float__To__zero = h4/ieee/num2roundmode (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Goal: h4/ieee/num2roundmode (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/ieee/float__To__zero
%   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_ieees_floatu_u_Tou_u_zerou_u_def]: h4/ieee/float__To__zero = h4/ieee/num2roundmode (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Goal: h4/ieee/num2roundmode (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/ieee/float__To__zero
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_Q145263,TV_Q145259]: ![V_f, V_g]: (![V_x]: s(TV_Q145259,happ(s(t_fun(TV_Q145263,TV_Q145259),V_f),s(TV_Q145263,V_x))) = s(TV_Q145259,happ(s(t_fun(TV_Q145263,TV_Q145259),V_g),s(TV_Q145263,V_x))) => s(t_fun(TV_Q145263,TV_Q145259),V_f) = s(t_fun(TV_Q145263,TV_Q145259),V_g))).
fof(ah4s_ieees_floatu_u_Tou_u_zerou_u_def, axiom, s(t_h4s_ieees_roundmode,h4s_ieees_floatu_u_tou_u_zero) = s(t_h4s_ieees_roundmode,h4s_ieees_num2roundmode(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ch4s_ieees_num2roundmodeu_u_thmu_c1, conjecture, s(t_h4s_ieees_roundmode,h4s_ieees_num2roundmode(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_ieees_roundmode,h4s_ieees_floatu_u_tou_u_zero)).
