|
(comparison1
(n_value_TCC1 0
(n_value_TCC1-1 nil 3507032124 ("" (tcc :defs !) nil nil)
((boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(number nonempty-type-decl nil numbers nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(rational nonempty-type-from-decl nil rationals nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(int nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(above nonempty-type-eq-decl nil integers nil)
(b formal-const-decl "above(1)" comparison1 nil)
(p formal-const-decl "above(1)" comparison1 nil)
(integer nonempty-type-from-decl nil integers nil)
(E_max formal-const-decl "integer" comparison1 nil)
(E_min formal-const-decl "{i: integer | E_max > i}" comparison1
nil)
(fp_num type-decl nil IEEE_854_values nil)
(finite? adt-recognizer-decl "[fp_num -> boolean]" IEEE_854_values
nil)
(infinite? adt-recognizer-decl "[fp_num -> boolean]"
IEEE_854_values nil)
(/= const-decl "boolean" notequal nil))
nil))
(n_value_TCC2 0
(n_value_TCC2-1 nil 3507032124
("" (skolem-typepred) (("" (ground) nil)) nil)
((infinite? adt-recognizer-decl "[fp_num -> boolean]"
IEEE_854_values nil)
(finite? adt-recognizer-decl "[fp_num -> boolean]" IEEE_854_values
nil)
(fp_num type-decl nil IEEE_854_values nil)
(E_min formal-const-decl "{i: integer | E_max > i}" comparison1
nil)
(E_max formal-const-decl "integer" comparison1 nil)
(integer nonempty-type-from-decl nil integers nil)
(p formal-const-decl "above(1)" comparison1 nil)
(b formal-const-decl "above(1)" comparison1 nil)
(above nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number nonempty-type-decl nil numbers nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(fp_compare_TCC1 0
(fp_compare_TCC1-1 nil 3507032124 ("" (tcc :defs !) nil nil) nil
nil))
(fp_compare_TCC2 0
(fp_compare_TCC2-1 nil 3507032124 ("" (tcc :defs !) nil nil) nil
nil))
(posinf_ge 0
(posinf_ge-1 nil 3507032124
("" (skolem-typepred)
(("" (prop)
(("1" (expand "pos")
(("1" (lemma "value_nonzero")
(("1" (inst?)
(("1" (hide 2)
(("1" (expand "fp_compare")
(("1" (assert)
(("1" (ground)
(("1" (lift-if)
(("1" (expand "n_value")
(("1" (rewrite "expt_x0")
(("1" (ground)
(("1" (case "max_pos < b^(1+E_max)")
(("1"
(expand "abs")
(("1" (lift-if) (("1" (ground) nil)))))
("2"
(hide -1 -2 -3 2)
(("2"
(lemma "max_fp_correct")
(("2"
(replace -1)
(("2"
(assert)
(("2"
(lemma "expt_pos")
(("2"
(inst-cp - "1+E_max" "b")
(("2"
(inst - "1+E_max-p" "b")
(("2"
(assert)
nil)))))))))))))))))))))))))
("2" (expand "n_value")
(("2" (rewrite "expt_x0")
(("2" (expand "zero?")
(("2" (assert)
(("2" (lemma "expt_pos")
(("2"
(inst?)
(("2"
(assert)
nil)))))))))))))))))))))))))))
("2" (expand "pos")
(("2" (expand "fp_compare")
(("2" (assert)
(("2" (lift-if)
(("2" (ground)
(("2" (hide -1 1 2 3)
(("2" (expand "n_value")
(("2" (typepred "i_sign(num!1)")
(("2" (ground)
(("2" (replace -1)
(("2" (rewrite "expt_x0")
(("2" (rewrite "expt_x1")
(("2"
(lemma "expt_pos")
(("2"
(inst?)
(("2"
(rewrite
"both_sides_times_pos_gt1")
nil))))))))))))))))))))))))))))))))
nil)
((value_nonzero formula-decl nil IEEE_854_values nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(zero? const-decl "bool" IEEE_854_values nil)
(expt_pos formula-decl nil exponentiation nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(expt_x0 formula-decl nil exponentiation nil)
(minus_odd_is_odd application-judgement "odd_int" integers nil)
(< const-decl "bool" reals nil) (>= const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(posreal nonempty-type-eq-decl nil real_types nil)
(max_pos const-decl "posreal" IEEE_854_values nil)
(/= const-decl "boolean" notequal nil)
(^ const-decl "real" exponentiation nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(max_fp_correct formula-decl nil IEEE_854_values nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(rat_minus_rat_is_rat application-judgement "rat" rationals nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(posrat_times_posrat_is_posrat application-judgement "posrat"
rationals nil)
(n_value const-decl "real" comparison1 nil)
(posrat_exp application-judgement "posrat" exponentiation nil)
(nnrat_exp application-judgement "nnrat" exponentiation nil)
(nzreal_exp application-judgement "nzreal" exponentiation nil)
(int_exp application-judgement "int" exponentiation nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(fp_compare const-decl "comparison_code" comparison1 nil)
(num!1 skolem-const-decl
"{fp: fp_num | finite?(fp) OR infinite?(fp)}" comparison1 nil)
(pos const-decl "sign_rep" enumerated_type_defs nil)
(i_sign adt-accessor-decl "[(infinite?) -> sign_rep]"
IEEE_854_values nil)
(sign_rep type-eq-decl nil enumerated_type_defs nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(expt_x1 formula-decl nil exponentiation nil)
(both_sides_times_pos_gt1 formula-decl nil real_props nil)
(nzrat_times_nzrat_is_nzrat application-judgement "nzrat" rationals
nil)
(infinite? adt-recognizer-decl "[fp_num -> boolean]"
IEEE_854_values nil)
(finite? adt-recognizer-decl "[fp_num -> boolean]" IEEE_854_values
nil)
(fp_num type-decl nil IEEE_854_values nil)
(E_min formal-const-decl "{i: integer | E_max > i}" comparison1
nil)
(E_max formal-const-decl "integer" comparison1 nil)
(integer nonempty-type-from-decl nil integers nil)
(p formal-const-decl "above(1)" comparison1 nil)
(b formal-const-decl "above(1)" comparison1 nil)
(above nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number nonempty-type-decl nil numbers nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(NaN_unordered 0
(NaN_unordered-1 nil 3507032124
("" (skosimp*)
(("" (expand "fp_compare")
(("" (assert) (("" (lift-if) (("" (ground) nil))))))))
nil)
((fp_compare const-decl "comparison_code" comparison1 nil)) nil))
(eq_def 0
(eq_def-1 nil 3507032124
("" (skolem-typepred)
(("" (expand "eq?")
(("" (expand "fp_compare")
(("" (lift-if) (("" (ground) nil))))))))
nil)
((eq? const-decl "bool" comparison1 nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(fp_compare const-decl "comparison_code" comparison1 nil)
(infinite? adt-recognizer-decl "[fp_num -> boolean]"
IEEE_854_values nil)
(finite? adt-recognizer-decl "[fp_num -> boolean]" IEEE_854_values
nil)
(fp_num type-decl nil IEEE_854_values nil)
(E_min formal-const-decl "{i: integer | E_max > i}" comparison1
nil)
(E_max formal-const-decl "integer" comparison1 nil)
(integer nonempty-type-from-decl nil integers nil)
(p formal-const-decl "above(1)" comparison1 nil)
(b formal-const-decl "above(1)" comparison1 nil)
(above nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number nonempty-type-decl nil numbers nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(ne_def 0
(ne_def-1 nil 3507032124
("" (skolem-typepred)
(("" (expand "ne?")
(("" (expand "fp_compare")
(("" (lift-if) (("" (ground) nil))))))))
nil)
((ne? const-decl "bool" comparison1 nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(fp_compare const-decl "comparison_code" comparison1 nil)
(infinite? adt-recognizer-decl "[fp_num -> boolean]"
IEEE_854_values nil)
(finite? adt-recognizer-decl "[fp_num -> boolean]" IEEE_854_values
nil)
(fp_num type-decl nil IEEE_854_values nil)
(E_min formal-const-decl "{i: integer | E_max > i}" comparison1
nil)
(E_max formal-const-decl "integer" comparison1 nil)
(integer nonempty-type-from-decl nil integers nil)
(p formal-const-decl "above(1)" comparison1 nil)
(b formal-const-decl "above(1)" comparison1 nil)
(above nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number nonempty-type-decl nil numbers nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(gt_def 0
(gt_def-1 nil 3507032124
("" (skolem-typepred)
(("" (expand "gt?")
(("" (expand "fp_compare")
(("" (lift-if) (("" (ground) nil))))))))
nil)
((gt? const-decl "bool" comparison1 nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(fp_compare const-decl "comparison_code" comparison1 nil)
(infinite? adt-recognizer-decl "[fp_num -> boolean]"
IEEE_854_values nil)
(finite? adt-recognizer-decl "[fp_num -> boolean]" IEEE_854_values
nil)
(fp_num type-decl nil IEEE_854_values nil)
(E_min formal-const-decl "{i: integer | E_max > i}" comparison1
nil)
(E_max formal-const-decl "integer" comparison1 nil)
(integer nonempty-type-from-decl nil integers nil)
(p formal-const-decl "above(1)" comparison1 nil)
(b formal-const-decl "above(1)" comparison1 nil)
(above nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number nonempty-type-decl nil numbers nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(ge_def 0
(ge_def-1 nil 3507032124
("" (skolem-typepred)
(("" (expand "ge?")
(("" (expand "fp_compare")
(("" (lift-if) (("" (ground) nil))))))))
nil)
((ge? const-decl "bool" comparison1 nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(fp_compare const-decl "comparison_code" comparison1 nil)
(infinite? adt-recognizer-decl "[fp_num -> boolean]"
IEEE_854_values nil)
(finite? adt-recognizer-decl "[fp_num -> boolean]" IEEE_854_values
nil)
(fp_num type-decl nil IEEE_854_values nil)
(E_min formal-const-decl "{i: integer | E_max > i}" comparison1
nil)
(E_max formal-const-decl "integer" comparison1 nil)
(integer nonempty-type-from-decl nil integers nil)
(p formal-const-decl "above(1)" comparison1 nil)
(b formal-const-decl "above(1)" comparison1 nil)
(above nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number nonempty-type-decl nil numbers nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(lt_def 0
(lt_def-1 nil 3507032124
("" (skolem-typepred)
(("" (expand "lt?")
(("" (expand "fp_compare")
(("" (lift-if) (("" (ground) nil))))))))
nil)
((lt? const-decl "bool" comparison1 nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(fp_compare const-decl "comparison_code" comparison1 nil)
(infinite? adt-recognizer-decl "[fp_num -> boolean]"
IEEE_854_values nil)
(finite? adt-recognizer-decl "[fp_num -> boolean]" IEEE_854_values
nil)
(fp_num type-decl nil IEEE_854_values nil)
(E_min formal-const-decl "{i: integer | E_max > i}" comparison1
nil)
(E_max formal-const-decl "integer" comparison1 nil)
(integer nonempty-type-from-decl nil integers nil)
(p formal-const-decl "above(1)" comparison1 nil)
(b formal-const-decl "above(1)" comparison1 nil)
(above nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number nonempty-type-decl nil numbers nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(le_def 0
(le_def-1 nil 3507032124
("" (skolem-typepred)
(("" (expand "le?")
(("" (expand "fp_compare")
(("" (lift-if) (("" (ground) nil))))))))
nil)
((le? const-decl "bool" comparison1 nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(fp_compare const-decl "comparison_code" comparison1 nil)
(infinite? adt-recognizer-decl "[fp_num -> boolean]"
IEEE_854_values nil)
(finite? adt-recognizer-decl "[fp_num -> boolean]" IEEE_854_values
nil)
(fp_num type-decl nil IEEE_854_values nil)
(E_min formal-const-decl "{i: integer | E_max > i}" comparison1
nil)
(E_max formal-const-decl "integer" comparison1 nil)
(integer nonempty-type-from-decl nil integers nil)
(p formal-const-decl "above(1)" comparison1 nil)
(b formal-const-decl "above(1)" comparison1 nil)
(above nonempty-type-eq-decl nil integers nil)
(> const-decl "bool" reals nil)
(int nonempty-type-eq-decl nil integers nil)
(integer_pred const-decl "[rational -> boolean]" integers nil)
(rational nonempty-type-from-decl nil rationals nil)
(rational_pred const-decl "[real -> boolean]" rationals nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number nonempty-type-decl nil numbers nil)
(OR const-decl "[bool, bool -> bool]" booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(un_def 0
(un_def-1 nil 3507032124
("" (skosimp*)
(("" (expand "un?")
(("" (expand "fp_compare")
(("" (lift-if) (("" (ground) nil))))))))
nil)
((un? const-decl "bool" comparison1 nil)
(fp_compare const-decl "comparison_code" comparison1 nil))
nil)))
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