%   ORIGINAL: h4/binary__ieee/neg__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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/binary__ieee/float__to__real__negate: !x. h4/binary__ieee/float__to__real (h4/binary__ieee/float__negate x) = h4/realax/real__neg (h4/binary__ieee/float__to__real x)
% Assm: h4/binary__ieee/ulp0: h4/binary__ieee/ulp h4/bool/the__value = h4/binary__ieee/float__to__real (h4/binary__ieee/float__plus__min h4/bool/the__value)
% Goal: h4/realax/real__neg (h4/binary__ieee/ulp h4/bool/the__value) = h4/binary__ieee/float__to__real (h4/binary__ieee/float__negate (h4/binary__ieee/float__plus__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_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_binaryu_u_ieees_floatu_u_tou_u_realu_u_negate]: !x. h4/binary__ieee/float__to__real (h4/binary__ieee/float__negate x) = h4/realax/real__neg (h4/binary__ieee/float__to__real x)
% Assm [h4s_binaryu_u_ieees_ulp0]: h4/binary__ieee/ulp h4/bool/the__value = h4/binary__ieee/float__to__real (h4/binary__ieee/float__plus__min h4/bool/the__value)
% Goal: h4/realax/real__neg (h4/binary__ieee/ulp h4/bool/the__value) = h4/binary__ieee/float__to__real (h4/binary__ieee/float__negate (h4/binary__ieee/float__plus__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_Q107157,TV_Q107153]: ![V_f, V_g]: (![V_x]: s(TV_Q107153,happ(s(t_fun(TV_Q107157,TV_Q107153),V_f),s(TV_Q107157,V_x))) = s(TV_Q107153,happ(s(t_fun(TV_Q107157,TV_Q107153),V_g),s(TV_Q107157,V_x))) => s(t_fun(TV_Q107157,TV_Q107153),V_f) = s(t_fun(TV_Q107157,TV_Q107153),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_binaryu_u_ieees_floatu_u_tou_u_realu_u_negate, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_realaxs_real,h4s_binaryu_u_ieees_floatu_u_tou_u_real(s(t_h4s_binaryu_u_ieees_float(TV_u_27a,TV_u_27b),h4s_binaryu_u_ieees_floatu_u_negate(s(t_h4s_binaryu_u_ieees_float(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_binaryu_u_ieees_floatu_u_tou_u_real(s(t_h4s_binaryu_u_ieees_float(TV_u_27a,TV_u_27b),V_x)))))).
fof(ah4s_binaryu_u_ieees_ulp0, axiom, ![TV_u_27t,TV_u_27w]: 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_floatu_u_tou_u_real(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_min(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value)))))).
fof(ch4s_binaryu_u_ieees_negu_u_ulp, conjecture, ![TV_u_27t,TV_u_27w]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(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_floatu_u_tou_u_real(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_negate(s(t_h4s_binaryu_u_ieees_float(TV_u_27t,TV_u_27w),h4s_binaryu_u_ieees_floatu_u_plusu_u_min(s(t_h4s_bools_itself(t_h4s_pairs_prod(TV_u_27t,TV_u_27w)),h4s_bools_theu_u_value)))))))).
