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Datei: Sprache: Lisp

Original von: PVS^©

(fp_round_aux
(Exp_of_TCC1 0
 (Exp_of_TCC1-1 nil 3321197030 ("" (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)
 (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 "boolean" notequal nil))
 nil))
(Exp_of_TCC2 0
 (Exp_of_TCC2-1 nil 3321197030 ("" (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)
 (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)
 (nonneg_real nonempty-type-eq-decl nil real_types nil)
 (> const-decl "bool" reals nil)
 (posreal nonempty-type-eq-decl nil real_types 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)
 (real_gt_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)
 (real_minus_real_is_real application-judgement "real" reals nil)
 (int_minus_int_is_int application-judgement "int" integers nil)
 (posnat_expt application-judgement "posnat" exponentiation nil)
 (posint_times_posint_is_posint application-judgement "posint"
 integers nil)
 (mult_divides1 application-judgement "(divides(n))" divides nil)
 (mult_divides2 application-judgement "(divides(m))" divides nil)
 (expt def-decl "real" exponentiation nil)
 (^ const-decl "real" exponentiation nil)
 (/= const-decl "boolean" notequal nil)
 (minus_int_is_int application-judgement "int" integers nil))
 nil))
(Exp_of_TCC3 0
 (Exp_of_TCC3-1 nil 3321197030
 (""
 (inst +
 "lambda (px:posreal): choose({i:int|b^i<=px & px)
 (("1" (skosimp*)
 (("1" (rewrite "nonempty_member")
 (("1" (expand "member")
 (("1" (lemma "exp_of_exists")
 (("1" (inst - "b" "px!1") (("1" (assert) nil)))))))
 ("2" (skosimp*) (("2" (assert) nil)))
 ("3" (skosimp*) (("3" (assert) nil)))))))
 ("2" (skosimp*) (("2" (assert) nil)))
 ("3" (skosimp*) (("3" (assert) nil))))
 nil)
 ((real_le_is_total_order name-judgement "(total_order?[real])"
 real_props nil)
 (nnrat_exp application-judgement "nnrat" exponentiation nil)
 (posrat_exp application-judgement "posrat" exponentiation nil)
 (member const-decl "bool" sets nil)
 (exp_of_exists formula-decl nil exponentiation nil)
 (nonempty_member formula-decl nil sets_lemmas nil)
 (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
 (choose const-decl "(p)" sets nil)
 (nonempty? const-decl "bool" sets nil)
 (set type-eq-decl nil sets nil)
 (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
 (numfield nonempty-type-eq-decl nil number_fields nil)
 (< const-decl "bool" reals nil)
 (b formal-const-decl "above(1)" fp_round_aux nil)
 (above nonempty-type-eq-decl nil integers nil)
 (^ const-decl "real" exponentiation nil)
 (/= const-decl "boolean" notequal nil)
 (OR const-decl "[bool, bool -> bool]" booleans nil)
 (<= const-decl "bool" reals nil)
 (AND const-decl "[bool, bool -> bool]" 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)
 (posreal nonempty-type-eq-decl nil real_types nil)
 (> const-decl "bool" reals 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)
 (int_plus_int_is_int application-judgement "int" integers nil))
 nil))
(Exp_of_correct_TCC1 0
 (Exp_of_correct_TCC1-1 nil 3321197030 ("" (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)
 (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)
 (nonneg_real nonempty-type-eq-decl nil real_types nil)
 (> const-decl "bool" reals nil)
 (posreal nonempty-type-eq-decl nil real_types nil)
 (real_gt_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)
 (/= const-decl "boolean" notequal nil))
 nil))
(Exp_of_correct 0
 (Exp_of_correct-1 nil 3321197030
 ("" (skosimp*)
 (("" (typepred "Exp_of(x!1)")
 (("1" (rewrite "expt_inverse")
 (("1" (assert)
 (("1" (lemma "expt_pos")
 (("1" (inst?)
 (("1" (rewrite "times_div1")
 (("1" (ground)
 (("1" (rewrite "div_mult_pos_le2") nil)
 ("2" (rewrite "div_mult_pos_lt1")
 (("2" (rewrite "expt_plus")
 (("2" (rewrite "expt_x1") nil)))))))))))))))))
 ("2" (skosimp*) (("2" (assert) nil)))
 ("3" (skosimp*) (("3" (assert) nil))))))
 nil)
 ((Exp_of const-decl "{i: int | b ^ i <= x & x numfield]" number_fields nil)
 (numfield nonempty-type-eq-decl nil number_fields nil)
 (< const-decl "bool" reals nil)
 (AND const-decl "[bool, bool -> bool]" booleans nil)
 (posreal nonempty-type-eq-decl nil real_types nil)
 (nonneg_real nonempty-type-eq-decl nil real_types nil)
 (b formal-const-decl "above(1)" fp_round_aux nil)
 (above nonempty-type-eq-decl nil integers nil)
 (> const-decl "bool" reals nil)
 (^ const-decl "real" exponentiation nil)
 (>= const-decl "bool" reals nil)
 (/= const-decl "boolean" notequal nil)
 (OR const-decl "[bool, bool -> bool]" 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)
 (<= 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)
 (posreal_times_posreal_is_posreal application-judgement "posreal"
 real_types nil)
 (int_plus_int_is_int application-judgement "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_gt_is_strict_total_order name-judgement
 "(strict_total_order?[real])" real_props nil)
 (div_mult_pos_le2 formula-decl nil real_props nil)
 (posrat_times_posrat_is_posrat application-judgement "posrat"
 rationals nil)
 (expt_plus formula-decl nil exponentiation nil)
 (int_minus_int_is_int application-judgement "int" integers nil)
 (posint_exp application-judgement "posint" exponentiation nil)
 (expt_x1 formula-decl nil exponentiation nil)
 (div_mult_pos_lt1 formula-decl nil real_props nil)
 (posreal_div_posreal_is_posreal application-judgement "posreal"
 real_types nil)
 (times_div1 formula-decl nil real_props nil)
 (nonzero_real nonempty-type-eq-decl nil reals nil)
 (expt_pos formula-decl nil exponentiation nil)
 (posrat_div_posrat_is_posrat application-judgement "posrat"
 rationals nil)
 (nnrat_exp application-judgement "nnrat" exponentiation nil)
 (posrat_exp application-judgement "posrat" exponentiation nil)
 (nzreal nonempty-type-eq-decl nil reals nil)
 (expt_inverse formula-decl nil exponentiation nil))
 nil))
(significand_TCC1 0
 (significand_TCC1-1 nil 3321197030 ("" (subtype-tcc) 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)
 (nzreal nonempty-type-eq-decl nil reals nil)
 (/= const-decl "boolean" notequal nil))
 nil))
(significand_TCC2 0
 (significand_TCC2-1 nil 3321197030
 ("" (skosimp*)
 (("" (assert)
 (("" (use "pos_times_gt")
 (("" (use "expt_pos")
 (("" (assert)
 (("" (assert)
 (("" (rewrite "Exp_of_correct") nil))))))))))))
 nil)
 ((minus_int_is_int application-judgement "int" integers nil)
 (nnrat_exp application-judgement "nnrat" exponentiation nil)
 (nonzero_abs_is_pos application-judgement "{y: posreal | y >= x}"
 real_defs nil)
 (posreal_times_posreal_is_posreal application-judgement "posreal"
 real_types nil)
 (real_le_is_total_order name-judgement "(total_order?[real])"
 real_props nil)
 (expt_pos formula-decl nil exponentiation nil)
 (Exp_of_correct formula-decl nil fp_round_aux nil)
 (real_gt_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)
 (number nonempty-type-decl nil numbers nil)
 (boolean nonempty-type-decl nil booleans 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)
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 (bool nonempty-type-eq-decl nil booleans nil)
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 (nonneg_real nonempty-type-eq-decl nil real_types nil)
 (AND const-decl "[bool, bool -> bool]" booleans nil)
 (numfield nonempty-type-eq-decl nil number_fields nil)
 (- const-decl "[numfield -> numfield]" number_fields nil)
 (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
 nil)
 (/= const-decl "boolean" notequal nil)
 (nzreal nonempty-type-eq-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)
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 (posreal nonempty-type-eq-decl nil real_types nil)
 (<= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
 (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
 (Exp_of const-decl "{i: int | b ^ i <= x & x < b ^ (i + 1)}"
 fp_round_aux nil)
 (pos_times_gt formula-decl nil real_props nil))
 nil))
(real_components_TCC1 0
 (real_components_TCC1-1 nil 3321197030 ("" (subtype-tcc) 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)
 (nzreal nonempty-type-eq-decl nil reals nil)
 (/= const-decl "boolean" notequal nil)
 (E const-decl "integer" fp_round_aux nil))
 nil))
(real_components 0
 (real_components-1 nil 3321197030
 ("" (skosimp*)
 (("" (expand "significand")
 (("" (expand "E")
 (("" (rewrite "associative_mult" :dir rl)
 (("" (rewrite "associative_mult" :dir rl)
 (("" (rewrite "associative_mult" :dir rl)
 (("" (rewrite "expt_plus" :dir rl)
 (("" (rewrite "expt_x0")
 (("" (grind) nil))))))))))))))))
 nil)
 ((significand const-decl "norm_fp_range" fp_round_aux nil)
 (nonzero_abs_is_pos application-judgement "{y: posreal | y >= x}"
 real_defs nil)
 (associative_mult formula-decl nil number_fields nil)
 (number nonempty-type-decl nil numbers nil)
 (boolean nonempty-type-decl nil booleans nil)
 (number_field_pred const-decl "[number -> boolean]" number_fields
 nil)
 (numfield nonempty-type-eq-decl nil number_fields nil)
 (number_field nonempty-type-from-decl nil number_fields nil)
 (real_pred const-decl "[number_field -> boolean]" reals nil)
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 (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)
 (sgn const-decl "int" real_defs nil)
 (/= const-decl "boolean" notequal nil)
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 (AND const-decl "[bool, bool -> bool]" booleans nil)
 (- const-decl "[numfield -> numfield]" number_fields nil)
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 nil)
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 (posreal nonempty-type-eq-decl nil real_types nil)
 (<= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
 (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
 (Exp_of const-decl "{i: int | b ^ i <= x & x < b ^ (i + 1)}"
 fp_round_aux nil)
 (posrat_exp application-judgement "posrat" exponentiation nil)
 (nnrat_exp application-judgement "nnrat" exponentiation nil)
 (posreal_times_posreal_is_posreal application-judgement "posreal"
 real_types nil)
 (real_times_real_is_real application-judgement "real" reals nil)
 (posrat_times_posrat_is_posrat application-judgement "posrat"
 rationals nil)
 (expt_x0 formula-decl nil exponentiation nil)
 (nzreal_times_nzreal_is_nzreal application-judgement "nzreal"
 real_types nil)
 (minus_odd_is_odd application-judgement "odd_int" integers nil)
 (real_ge_is_total_order name-judgement "(total_order?[real])"
 real_props nil)
 (minus_nzreal_is_nzreal application-judgement "nzreal" real_types
 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)
 (expt_plus formula-decl nil exponentiation nil)
 (minus_int_is_int application-judgement "int" integers nil)
 (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
 (E const-decl "integer" fp_round_aux nil))
 nil))
(abs_real_components 0
 (abs_real_components-1 nil 3321197030
 ("" (skosimp*)
 (("" (use "real_components")
 (("" (expand "abs")
 (("" (expand "sgn")
 (("" (lift-if) (("" (assert) (("" (ground) nil))))))))))))
 nil)
 ((real_components formula-decl nil fp_round_aux nil)
 (nzreal nonempty-type-eq-decl nil reals nil)
 (/= const-decl "boolean" notequal 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)
 (nnrat_exp application-judgement "nnrat" exponentiation nil)
 (posrat_exp application-judgement "posrat" exponentiation nil)
 (rat_times_rat_is_rat application-judgement "rat" rationals nil)
 (nonzero_abs_is_pos application-judgement "{y: posreal | y >= x}"
 real_defs nil)
 (posreal_times_posreal_is_posreal application-judgement "posreal"
 real_types nil)
 (sgn const-decl "int" real_defs 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)
 (minus_nzreal_is_nzreal application-judgement "nzreal" real_types
 nil)
 (nzreal_times_nzreal_is_nzreal application-judgement "nzreal"
 real_types nil)
 (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
 nil))
 nil))
(Exp_of_unique_TCC1 0
 (Exp_of_unique_TCC1-1 nil 3321197030 ("" (subtype-tcc) 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)
 (rational_pred const-decl "[real -> boolean]" rationals nil)
 (rational nonempty-type-from-decl nil rationals nil)
 (integer_pred const-decl "[rational -> boolean]" integers nil)
 (integer nonempty-type-from-decl nil integers nil)
 (>= const-decl "bool" reals nil)
 (nonneg_real nonempty-type-eq-decl nil real_types nil)
 (> const-decl "bool" reals nil)
 (posreal nonempty-type-eq-decl nil real_types 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_le_is_total_order name-judgement "(total_order?[real])"
 real_props nil)
 (nat_exp application-judgement "nat" exponentiation 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)
 (/= const-decl "boolean" notequal nil))
 nil))
(Exp_of_unique_TCC2 0
 (Exp_of_unique_TCC2-1 nil 3321197030 ("" (subtype-tcc) 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)
 (rational_pred const-decl "[real -> boolean]" rationals nil)
 (rational nonempty-type-from-decl nil rationals nil)
 (integer_pred const-decl "[rational -> boolean]" integers nil)
 (integer nonempty-type-from-decl nil integers nil)
 (>= const-decl "bool" reals nil)
 (nonneg_real nonempty-type-eq-decl nil real_types nil)
 (> const-decl "bool" reals nil)
 (posreal nonempty-type-eq-decl nil real_types nil)
 (real_minus_real_is_real application-judgement "real" reals 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_le_is_total_order name-judgement "(total_order?[real])"
 real_props nil)
 (nat_exp application-judgement "nat" exponentiation 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)
 (/= const-decl "boolean" notequal nil))
 nil))
(Exp_of_unique 0
 (Exp_of_unique-1 nil 3321197030
 ("" (skosimp*)
 (("" (case "b^i!1 < b^(1+j!1) & b^j!1 < b^(1+i!1)")
 (("1" (hide -2 -3 -4 -5)
 (("1" (flatten)
 (("1" (rewrite "both_sides_expt_gt1_lt")
 (("1" (rewrite "both_sides_expt_gt1_lt")
 (("1" (assert) nil)))))))))
 ("2" (assert) nil) ("3" (assert) nil) ("4" (assert) nil)
 ("5" (assert) nil) ("6" (assert) nil))))
 nil)
 ((+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
 (numfield nonempty-type-eq-decl nil number_fields nil)
 (integer nonempty-type-from-decl nil integers nil)
 (b formal-const-decl "above(1)" fp_round_aux nil)
 (above nonempty-type-eq-decl nil integers nil)
 (> const-decl "bool" reals nil)
 (^ const-decl "real" exponentiation nil)
 (>= const-decl "bool" reals nil)
 (/= const-decl "boolean" notequal nil)
 (OR const-decl "[bool, bool -> bool]" 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)
 (< 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)
 (AND const-decl "[bool, bool -> bool]" booleans nil)
 (bool nonempty-type-eq-decl nil booleans nil)
 (boolean nonempty-type-decl nil booleans nil)
 (int_plus_int_is_int application-judgement "int" integers nil)
 (real_lt_is_strict_total_order name-judgement
 "(strict_total_order?[real])" real_props nil)
 (nnrat_exp application-judgement "nnrat" exponentiation nil)
 (posrat_exp application-judgement "posrat" exponentiation nil)
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 nil))
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 nil))
 nil))
 nil))
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 nil))
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(truncate_shift 0
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 ("" (skosimp*)
 (("" (apply-extensionality)
 (("1" (hide 2)
 (("1" (expand "truncate")
 (("1" (rewrite "associative_mult")
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 ("2" (hide 2)
 (("2" (use "expt_pos")
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 (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
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(Exp_of_shift 0
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 ("" (skosimp*)
 (("" (lemma "Exp_of_unique")
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 (< const-decl "bool" reals nil)
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 real_props nil)
 (real_gt_is_strict_total_order name-judgement
 "(strict_total_order?[real])" real_props nil)
 (commutative_mult formula-decl nil number_fields nil)
 (div_mult_pos_lt2 formula-decl nil real_props nil)
 (int_minus_int_is_int application-judgement "int" integers nil)
 (expt_div formula-decl nil exponentiation nil)
 (nzreal nonempty-type-eq-decl nil reals nil)
 (posrat_div_posrat_is_posrat application-judgement "posrat"
 rationals nil)
 (div_mult_pos_le1 formula-decl nil real_props nil)
 (real_ge_is_total_order name-judgement "(total_order?[real])"
 real_props nil)
 (number nonempty-type-decl nil numbers nil)
 (boolean nonempty-type-decl nil booleans 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)
 (integer nonempty-type-from-decl nil integers nil)
 (bool nonempty-type-eq-decl nil booleans nil)
 (>= const-decl "bool" reals nil)
 (nonneg_real nonempty-type-eq-decl nil real_types nil)
 (> const-decl "bool" reals nil)
 (posreal nonempty-type-eq-decl nil real_types nil)
 (above nonempty-type-eq-decl nil integers nil)
 (b formal-const-decl "above(1)" fp_round_aux nil)
 (expt_pos formula-decl nil exponentiation nil)
 (posrat_exp application-judgement "posrat" exponentiation nil)
 (nnrat_exp application-judgement "nnrat" exponentiation nil))
 nil))
(scale_shift 0
 (scale_shift-1 nil 3321197030
 ("" (skosimp*)
 (("" (expand "scale") (("" (rewrite "Exp_of_shift") nil)))) nil)
 ((scale const-decl
 "{i: int | b ^ (i + p - 1) <= x & x const-decl "bool" reals nil)
 (nonneg_real nonempty-type-eq-decl nil real_types nil)
 (>= const-decl "bool" reals nil)
 (bool nonempty-type-eq-decl nil 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)
 (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)
 (Exp_of_shift formula-decl nil fp_round_aux nil)
 (int_plus_int_is_int application-judgement "int" integers nil)
 (posrat_exp application-judgement "posrat" exponentiation nil)
 (nnrat_exp application-judgement "nnrat" exponentiation nil)
 (int_minus_int_is_int application-judgement "int" integers nil))
 nil)))

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