%   ORIGINAL: h4/binary__ieee/min__properties_c8
% 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/binary__ieee/float__value__case__def_c0: !v1 v f a. h4/binary__ieee/float__value__CASE (h4/binary__ieee/Float a) f v v1 = f a
% Assm: h4/binary__ieee/float__is__finite__def: !x. h4/binary__ieee/float__is__finite x <=> h4/binary__ieee/float__value__CASE (h4/binary__ieee/float__value0 x) (\v1. T) F F
% Assm: h4/binary__ieee/float__values_c6: h4/binary__ieee/float__value0 (h4/binary__ieee/float__minus__min h4/bool/the__value) = h4/binary__ieee/Float (h4/real/_2F (h4/realax/real__neg (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) (h4/real/pow (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/arithmetic/_2B (h4/words/INT__MAX h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value))))
% Goal: h4/binary__ieee/float__is__finite (h4/binary__ieee/float__minus__min 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_binaryu_u_ieees_floatu_u_valueu_u_caseu_u_defu_c0]: !v1 v f a. h4/binary__ieee/float__value__CASE (h4/binary__ieee/Float a) f v v1 = happ f a
% Assm [h4s_binaryu_u_ieees_floatu_u_isu_u_finiteu_u_def]: !_0. (!v1. happ _0 v1 <=> T) ==> (!x. h4/binary__ieee/float__is__finite x <=> h4/binary__ieee/float__value__CASE (h4/binary__ieee/float__value0 x) _0 F F)
% Assm [h4s_binaryu_u_ieees_floatu_u_valuesu_c6]: h4/binary__ieee/float__value0 (h4/binary__ieee/float__minus__min h4/bool/the__value) = h4/binary__ieee/Float (h4/real/_2F (h4/realax/real__neg (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) (h4/real/pow (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/arithmetic/_2B (h4/words/INT__MAX h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value))))
% Goal: h4/binary__ieee/float__is__finite (h4/binary__ieee/float__minus__min 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_Q106608,TV_Q106604]: ![V_f, V_g]: (![V_x]: s(TV_Q106604,happ(s(t_fun(TV_Q106608,TV_Q106604),V_f),s(TV_Q106608,V_x))) = s(TV_Q106604,happ(s(t_fun(TV_Q106608,TV_Q106604),V_g),s(TV_Q106608,V_x))) => s(t_fun(TV_Q106608,TV_Q106604),V_f) = s(t_fun(TV_Q106608,TV_Q106604),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_binaryu_u_ieees_floatu_u_valueu_u_caseu_u_defu_c0, axiom, ![TV_u_27a]: ![V_v1, V_v, V_f, V_a]: s(TV_u_27a,h4s_binaryu_u_ieees_floatu_u_valueu_u_case(s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_float(s(t_h4s_realaxs_real,V_a))),s(t_fun(t_h4s_realaxs_real,TV_u_27a),V_f),s(TV_u_27a,V_v),s(TV_u_27a,V_v1))) = s(TV_u_27a,happ(s(t_fun(t_h4s_realaxs_real,TV_u_27a),V_f),s(t_h4s_realaxs_real,V_a)))).
fof(ah4s_binaryu_u_ieees_floatu_u_isu_u_finiteu_u_def, axiom, ![TV_u_27t,TV_u_27w]: ![V_uu_0]: (![V_v1]: s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),V_uu_0),s(t_h4s_realaxs_real,V_v1))) = s(t_bool,t) => ![V_x]: s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_finite(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))) = s(t_bool,h4s_binaryu_u_ieees_floatu_u_valueu_u_case(s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_floatu_u_value0(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),V_x))),s(t_fun(t_h4s_realaxs_real,t_bool),V_uu_0),s(t_bool,f),s(t_bool,f))))).
fof(ah4s_binaryu_u_ieees_floatu_u_valuesu_c6, axiom, ![TV_u_27w,TV_u_27t]: s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_floatu_u_value0(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_min(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))) = s(t_h4s_binaryu_u_ieees_floatu_u_value,h4s_binaryu_u_ieees_float(s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_wordss_intu_u_max(s(t_h4s_bools_itself(TV_u_27w),h4s_bools_theu_u_value))),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27t),h4s_bools_theu_u_value)))))))))))).
fof(ch4s_binaryu_u_ieees_minu_u_propertiesu_c8, conjecture, ![TV_u_27t,TV_u_27w]: p(s(t_bool,h4s_binaryu_u_ieees_floatu_u_isu_u_finite(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_minusu_u_min(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value))))))).
