|
(bisection_nat_sqrt
(fs_lt_def 0
(fs_lt_def-1 nil 3394267943 ("" (grind) nil nil)
((boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[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)
(>= const-decl "bool" 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)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(sq const-decl "nonneg_real" sq "reals/")
(fs_lt? const-decl "bool" bisection_nat_sqrt nil)
(fs_eq? const-decl "bool" bisection_nat_sqrt nil)
(fs_gt? const-decl "bool" bisection_nat_sqrt nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil))
shostak))
(fs_eq_def 0
(fs_eq_def-1 nil 3394267949 ("" (grind) nil nil)
((boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[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)
(>= const-decl "bool" 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)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(sq const-decl "nonneg_real" sq "reals/")
(fs_eq? const-decl "bool" bisection_nat_sqrt nil)
(fs_lt? const-decl "bool" bisection_nat_sqrt nil)
(fs_gt? const-decl "bool" bisection_nat_sqrt nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil))
shostak))
(fs_gt_def 0
(fs_gt_def-1 nil 3394267959 ("" (grind) nil nil)
((boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[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)
(>= const-decl "bool" 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)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(sq const-decl "nonneg_real" sq "reals/")
(fs_gt? const-decl "bool" bisection_nat_sqrt nil)
(fs_lt? const-decl "bool" bisection_nat_sqrt nil)
(fs_eq? const-decl "bool" bisection_nat_sqrt nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil))
shostak))
(fs_trichotomy 0
(fs_trichotomy-1 nil 3394267964 ("" (grind) nil nil)
((boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[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)
(>= const-decl "bool" 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)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(mult_divides2 application-judgement "(divides(m))" divides nil)
(even_times_int_is_even application-judgement "even_int" integers
nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(sq const-decl "nonneg_real" sq "reals/")
(fs_lt? const-decl "bool" bisection_nat_sqrt nil)
(fs_eq? const-decl "bool" bisection_nat_sqrt nil)
(fs_gt? const-decl "bool" bisection_nat_sqrt nil)
(nnint_times_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(mult_divides1 application-judgement "(divides(n))" divides nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil))
shostak))
(fs_le_ge 0
(fs_le_ge-1 nil 3394269618
("" (skosimp)
(("" (expand "fs_le?")
(("" (expand "fs_ge?")
(("" (expand "fs_lt?")
(("" (expand "fs_eq?")
(("" (expand "fs_gt?")
(("" (split -1)
(("1" (split)
(("1" (flatten)
(("1" (lemma "sq_lt" ("nna" "1+m!1" "nnb" "1+n!1"))
(("1" (assert) nil nil)) nil))
nil)
("2" (lemma "sq_lt" ("nna" "1+m!1" "nnb" "n!1"))
(("2" (assert) nil nil)) nil))
nil)
("2" (split)
(("1" (flatten)
(("1" (lemma "sq_lt" ("nna" "n!1" "nnb" "1+m!1"))
(("1" (lemma "sq_lt" ("nna" "m!1" "nnb" "1+n!1"))
(("1" (assert) nil nil)) nil))
nil))
nil)
("2" (flatten)
(("2" (lemma "sq_lt" ("nna" "m!1" "nnb" "n!1"))
(("2" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((fs_le? const-decl "bool" bisection_nat_sqrt nil)
(fs_lt? const-decl "bool" bisection_nat_sqrt nil)
(fs_gt? const-decl "bool" bisection_nat_sqrt nil)
(nat nonempty-type-eq-decl nil naturalnumbers 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)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans 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)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(sq_lt formula-decl nil sq "reals/")
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(sq_nz_pos application-judgement "posreal" sq "reals/")
(fs_eq? const-decl "bool" bisection_nat_sqrt nil)
(fs_ge? const-decl "bool" bisection_nat_sqrt nil))
shostak))
(bisection_sqrt_aux_TCC1 0
(bisection_sqrt_aux_TCC1-1 nil 3394269004
("" (skosimp)
(("" (typepred "m!1")
(("" (typepred "n!1")
(("" (lemma "fs_le_ge" ("x" "x!1" "m" "m!1" "n" "n!1"))
(("" (assert) nil nil)) nil))
nil))
nil))
nil)
((fs_le? const-decl "bool" bisection_nat_sqrt nil)
(nat nonempty-type-eq-decl nil naturalnumbers 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)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(fs_le_ge formula-decl nil bisection_nat_sqrt nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(fs_ge? const-decl "bool" bisection_nat_sqrt nil))
nil))
(bisection_sqrt_aux_TCC2 0
(bisection_sqrt_aux_TCC2-1 nil 3394269004
("" (skosimp*)
(("" (typepred "t!1")
(("" (assert)
(("" (expand "fs_le?")
(("" (flatten)
(("" (expand "fs_lt?")
(("" (expand "fs_eq?") (("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil)
((< const-decl "bool" reals nil)
(fs_ge? const-decl "bool" bisection_nat_sqrt nil)
(fs_le? const-decl "bool" bisection_nat_sqrt nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(int nonempty-type-eq-decl nil integers nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(integer nonempty-type-from-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)
(<= const-decl "bool" reals 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)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil))
nil))
(bisection_sqrt_aux_TCC3 0
(bisection_sqrt_aux_TCC3-1 nil 3394269004
("" (skosimp*)
(("" (typepred "m!1")
(("" (typepred "n!1")
(("" (lemma "nonneg_floor_is_nat" ("x" "(n!1+m!1)/2"))
(("" (assert)
(("" (hide-all-but (-4 2))
(("" (expand "fs_le?")
(("" (expand "fs_lt?")
(("" (flatten)
(("" (expand "fs_eq?")
(("" (replace -1) (("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((fs_le? const-decl "bool" bisection_nat_sqrt nil)
(nat nonempty-type-eq-decl nil naturalnumbers 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)
(NOT const-decl "[bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(nonneg_floor_is_nat judgement-tcc nil floor_ceil nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(fs_lt? const-decl "bool" bisection_nat_sqrt nil)
(fs_eq? const-decl "bool" bisection_nat_sqrt nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(fs_ge? const-decl "bool" bisection_nat_sqrt nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil))
nil))
(bisection_sqrt_aux_TCC4 0
(bisection_sqrt_aux_TCC4-1 nil 3394269004
("" (skosimp*)
(("" (lemma "fs_le_ge" ("x" "x!1" "m" "m!1" "n" "n!1"))
(("" (assert) nil nil)) nil))
nil)
((fs_ge? const-decl "bool" bisection_nat_sqrt nil)
(fs_le? const-decl "bool" bisection_nat_sqrt nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans 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)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(fs_le_ge formula-decl nil bisection_nat_sqrt nil)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil))
nil))
(bisection_sqrt_aux_TCC5 0
(bisection_sqrt_aux_TCC5-1 nil 3394269004
("" (skosimp*)
(("" (lemma "fs_le_ge" ("x" "x!1" "m" "m!1" "n" "n!1"))
(("" (lemma "nonneg_floor_is_nat" ("x" "(n!1+m!1)/2"))
(("" (assert)
(("" (expand "fs_eq?")
(("" (expand "fs_lt?")
(("" (expand "fs_ge?")
(("" (expand "fs_gt?") (("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((fs_ge? const-decl "bool" bisection_nat_sqrt nil)
(fs_le? const-decl "bool" bisection_nat_sqrt nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans 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)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(fs_le_ge formula-decl nil bisection_nat_sqrt nil)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(fs_lt? const-decl "bool" bisection_nat_sqrt nil)
(fs_gt? const-decl "bool" bisection_nat_sqrt nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(fs_eq? const-decl "bool" bisection_nat_sqrt nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(nonneg_floor_is_nat judgement-tcc nil floor_ceil nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(/= const-decl "boolean" notequal nil)
(nznum nonempty-type-eq-decl nil number_fields nil)
(/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil))
nil))
(bisection_sqrt_aux_TCC6 0
(bisection_sqrt_aux_TCC6-1 nil 3413715945
("" (skosimp*)
(("" (lemma "fs_le_ge" ("x" "x!1" "m" "m!1" "n" "n!1"))
(("" (assert) nil nil)) nil))
nil)
((fs_ge? const-decl "bool" bisection_nat_sqrt nil)
(fs_le? const-decl "bool" bisection_nat_sqrt nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans 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)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(fs_le_ge formula-decl nil bisection_nat_sqrt nil)
(nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
(nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
rationals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil))
nil))
(bisection_sqrt_aux_prop 0
(bisection_sqrt_aux_prop-1 nil 3412657227
(""
(case "FORALL (k,m, n, x: nat):
n-m<=k & fs_le?(x)(m) AND fs_ge?(x)(n) =>
fs_eq?(x, bisection_sqrt_aux(x, m, n))")
(("1" (skosimp)
(("1" (inst - "n!1-m!1" "m!1" "n!1" "x!1")
(("1" (assert) nil nil)
("2" (assert)
(("2" (hide 2)
(("2" (expand "fs_le?")
(("2" (expand "fs_ge?")
(("2" (expand "fs_eq?")
(("2" (expand "fs_lt?")
(("2" (expand "fs_gt?")
(("2" (split)
(("1" (split)
(("1" (flatten)
(("1"
(lemma "sq_lt"
("nna" "1+m!1" "nnb" "1+n!1"))
(("1" (assert) nil nil)) nil))
nil)
("2"
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shostak))
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(bisection_sqrt_def 0
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(>= const-decl "bool" reals nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil))
shostak)))
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