%   ORIGINAL: h4/binary__ieee/ulp__lt__ULP
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/real/REAL__LE__REFL: !x. h4/real/real__lte x x
% Assm: h4/words/WORD__0__LS: !w. h4/words/word__ls (h4/words/n2w h4/num/0) w
% Assm: h4/binary__ieee/ulp__def: h4/binary__ieee/ulp h4/bool/the__value = h4/binary__ieee/ULP (h4/pair/_2C (h4/words/n2w h4/num/0) h4/bool/the__value)
% Assm: h4/binary__ieee/ULP__le__mono: !e2 e1. ~(e2 = h4/words/n2w h4/num/0) ==> (h4/real/real__lte (h4/binary__ieee/ULP (h4/pair/_2C e1 h4/bool/the__value)) (h4/binary__ieee/ULP (h4/pair/_2C e2 h4/bool/the__value)) <=> h4/words/word__ls e1 e2)
% Goal: !e. h4/real/real__lte (h4/binary__ieee/ulp h4/bool/the__value) (h4/binary__ieee/ULP (h4/pair/_2C e h4/bool/the__value))
%   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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_reals_REALu_u_LEu_u_REFL]: !x. h4/real/real__lte x x
% Assm [h4s_wordss_WORDu_u_0u_u_LS]: !w. h4/words/word__ls (h4/words/n2w h4/num/0) w
% Assm [h4s_binaryu_u_ieees_ulpu_u_def]: h4/binary__ieee/ulp h4/bool/the__value = h4/binary__ieee/ULP (h4/pair/_2C (h4/words/n2w h4/num/0) h4/bool/the__value)
% Assm [h4s_binaryu_u_ieees_ULPu_u_leu_u_mono]: !e2 e1. ~(e2 = h4/words/n2w h4/num/0) ==> (h4/real/real__lte (h4/binary__ieee/ULP (h4/pair/_2C e1 h4/bool/the__value)) (h4/binary__ieee/ULP (h4/pair/_2C e2 h4/bool/the__value)) <=> h4/words/word__ls e1 e2)
% Goal: !e. h4/real/real__lte (h4/binary__ieee/ulp h4/bool/the__value) (h4/binary__ieee/ULP (h4/pair/_2C e h4/bool/the__value))
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_Q107208,TV_Q107204]: ![V_f, V_g]: (![V_x]: s(TV_Q107204,happ(s(t_fun(TV_Q107208,TV_Q107204),V_f),s(TV_Q107208,V_x))) = s(TV_Q107204,happ(s(t_fun(TV_Q107208,TV_Q107204),V_g),s(TV_Q107208,V_x))) => s(t_fun(TV_Q107208,TV_Q107204),V_f) = s(t_fun(TV_Q107208,TV_Q107204),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
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_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_reals_REALu_u_LEu_u_REFL, axiom, ![V_x]: p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_x))))).
fof(ah4s_wordss_WORDu_u_0u_u_LS, axiom, ![TV_u_27a]: ![V_w]: p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))).
fof(ah4s_binaryu_u_ieees_ulpu_u_def, axiom, ![TV_u_27w,TV_u_27t]: s(t_h4s_realaxs_real,h4s_binaryu_u_ieees_ulp(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))) = s(t_h4s_realaxs_real,h4s_binaryu_u_ieees_ulp0(s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_bools_itself(TV_u_27t)),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,TV_u_27w),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_bools_itself(TV_u_27t),h4s_bools_theu_u_value)))))).
fof(ah4s_binaryu_u_ieees_ULPu_u_leu_u_mono, axiom, ![TV_u_27t,TV_u_27a]: ![V_e2, V_e1]: (~ (s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_e2) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))) => s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_binaryu_u_ieees_ulp0(s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_bools_itself(TV_u_27t)),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_e1),s(t_h4s_bools_itself(TV_u_27t),h4s_bools_theu_u_value))))),s(t_h4s_realaxs_real,h4s_binaryu_u_ieees_ulp0(s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_bools_itself(TV_u_27t)),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_e2),s(t_h4s_bools_itself(TV_u_27t),h4s_bools_theu_u_value))))))) = s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_e1),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_e2))))).
fof(ch4s_binaryu_u_ieees_ulpu_u_ltu_u_ULP, conjecture, ![TV_u_27w,TV_u_27t]: ![V_e]: p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_binaryu_u_ieees_ulp(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))),s(t_h4s_realaxs_real,h4s_binaryu_u_ieees_ulp0(s(t_h4s_pairs_prod(t_h4s_fcps_cart(t_bool,TV_u_27w),t_h4s_bools_itself(TV_u_27t)),h4s_pairs_u_2c(s(t_h4s_fcps_cart(t_bool,TV_u_27w),V_e),s(t_h4s_bools_itself(TV_u_27t),h4s_bools_theu_u_value))))))))).
