%   ORIGINAL: h4/ieee/num2roundmode__roundmode2num
% 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/roundmode__BIJ_c0: !a. h4/ieee/num2roundmode (h4/ieee/roundmode2num a) = a
% Goal: !a. h4/ieee/num2roundmode (h4/ieee/roundmode2num a) = a
%   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_roundmodeu_u_BIJu_c0]: !a. h4/ieee/num2roundmode (h4/ieee/roundmode2num a) = a
% Goal: !a. h4/ieee/num2roundmode (h4/ieee/roundmode2num a) = a
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_Q145088,TV_Q145084]: ![V_f, V_g]: (![V_x]: s(TV_Q145084,happ(s(t_fun(TV_Q145088,TV_Q145084),V_f),s(TV_Q145088,V_x))) = s(TV_Q145084,happ(s(t_fun(TV_Q145088,TV_Q145084),V_g),s(TV_Q145088,V_x))) => s(t_fun(TV_Q145088,TV_Q145084),V_f) = s(t_fun(TV_Q145088,TV_Q145084),V_g))).
fof(ah4s_ieees_roundmodeu_u_BIJu_c0, axiom, ![V_a]: s(t_h4s_ieees_roundmode,h4s_ieees_num2roundmode(s(t_h4s_nums_num,h4s_ieees_roundmode2num(s(t_h4s_ieees_roundmode,V_a))))) = s(t_h4s_ieees_roundmode,V_a)).
fof(ch4s_ieees_num2roundmodeu_u_roundmode2num, conjecture, ![V_a]: s(t_h4s_ieees_roundmode,h4s_ieees_num2roundmode(s(t_h4s_nums_num,h4s_ieees_roundmode2num(s(t_h4s_ieees_roundmode,V_a))))) = s(t_h4s_ieees_roundmode,V_a)).
