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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: inset.C   Sprache: C

Original von: PVS©

(float (vNum_TCC1 0
        (vNum_TCC1-1 nil 3321636413 ("" (subtype-tcc) nil nil)
         ((/= const-decl "boolean" notequal nil)) nil))
       (radix_div_vNum 0
        (radix_div_vNum-1 nil 3319366647
         ("" (judgement-tcc)
          ((""
            (case-replace
             "expt(radix, Prec(b!1)) / radix=expt(radix, Prec(b!1)-1)")
            (("1" (grind-reals) nil nil)
             ("2" (hide 2)
              (("2" (rewrite "expt_minus_aux")
                (("2" (rewrite "expt_x1_aux"nil nil)) nil))
              nil))
            nil))
          nil)
         ((int_minus_int_is_int application-judgement "int" integers
           nil)
          (number nonempty-type-decl nil numbers nil)
          (boolean nonempty-type-decl nil booleans nil)
          (= const-decl "[T, T -> boolean]" equalities 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)
          (/= const-decl "boolean" notequal nil)
          (nznum nonempty-type-eq-decl nil number_fields nil)
          (/ const-decl "[numfield, nznum -> numfield]" 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)
          (bool nonempty-type-eq-decl nil booleans nil)
          (>= const-decl "bool" reals nil)
          (nat nonempty-type-eq-decl nil naturalnumbers nil)
          (expt def-decl "real" exponentiation nil)
          (> const-decl "bool" reals nil)
          (above nonempty-type-eq-decl nil integers nil)
          (radix formal-const-decl "above(1)" float nil)
          (Format type-eq-decl nil float nil)
          (- const-decl "[numfield, numfield -> numfield]"
             number_fields nil)
          (nzreal nonempty-type-eq-decl nil reals nil)
          (expt_minus_aux formula-decl nil exponentiation nil)
          (expt_x1_aux formula-decl nil exponentiation nil)
          (posnat_expt application-judgement "posnat" exponentiation
           nil)
          (^ const-decl "real" exponentiation nil)
          (real_ge_is_total_order name-judgement "(total_order?[real])"
           real_props nil)
          (posrat_div_posrat_is_posrat application-judgement "posrat"
           rationals nil)
          (posint_exp application-judgement "posint" exponentiation
           nil)
          (vNum const-decl "posnat" float nil))
         nil))
       (radix_less_vNum 0
        (radix_less_vNum-1 nil 3319366647
         ("" (judgement-tcc)
          (("" (lemma "both_sides_expt_gt1_ge_aux")
            (("" (inst -1 "radix" "Prec(b!1)-1" "0")
              (("" (grind-reals)
                (("" (rewrite "expt_x1_aux" -1) (("" (assertnil nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ((both_sides_expt_gt1_ge_aux formula-decl nil exponentiation
           nil)
          (int_plus_int_is_int application-judgement "int" integers
           nil)
          (nnint_plus_posint_is_posint application-judgement "posint"
           integers nil)
          (even_plus_odd_is_odd application-judgement "odd_int"
           integers nil)
          (expt_x1_aux formula-decl nil exponentiation nil)
          (Format type-eq-decl nil float nil)
          (- const-decl "[numfield, numfield -> numfield]"
             number_fields nil)
          (numfield nonempty-type-eq-decl nil number_fields nil)
          (nat nonempty-type-eq-decl nil naturalnumbers nil)
          (radix formal-const-decl "above(1)" float nil)
          (above nonempty-type-eq-decl nil integers 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_minus_int_is_int application-judgement "int" integers
           nil)
          (real_gt_is_strict_total_order name-judgement
           "(strict_total_order?[real])" real_props nil)
          (posnat_expt application-judgement "posnat" exponentiation
           nil)
          (^ const-decl "real" exponentiation nil)
          (real_ge_is_total_order name-judgement "(total_order?[real])"
           real_props nil)
          (posint_exp application-judgement "posint" exponentiation
           nil)
          (real_le_is_total_order name-judgement "(total_order?[real])"
           real_props nil)
          (vNum const-decl "posnat" float nil))
         nil))
       (FtoR_TCC1 0
        (FtoR_TCC1-1 nil 3318615387 ("" (subtype-tcc) nil nil)
         ((/= const-decl "boolean" notequal nil)) nil))
       (float_int_def 0
        (float_int_def-1 nil 3544780855 ("" (grind) nil nil)
         ((float_int const-decl "float" float nil)
          (expt def-decl "real" exponentiation nil)
          (^ const-decl "real" exponentiation nil)
          (FtoR const-decl "real" float nil))
         shostak))
       (Fplus_TCC1 0
        (Fplus_TCC1-1 nil 3319889173 ("" (subtype-tcc) nil nil)
         ((/= const-decl "boolean" notequal nil)
          (int_min application-judgement "{k: int | k <= i AND k <= j}"
           real_defs nil))
         nil))
       (Fplus_TCC2 0
        (Fplus_TCC2-1 nil 3319889173 ("" (subtype-tcc) nil nil)
         ((/= const-decl "boolean" notequal nil)
          (int_min application-judgement "{k: int | k <= i AND k <= j}"
           real_defs nil))
         nil))
       (Fplus_TCC3 0
        (Fplus_TCC3-1 nil 3319889173 ("" (subtype-tcc) nil nil)
         ((^ const-decl "real" exponentiation nil)
          (int_plus_int_is_int application-judgement "int" integers
           nil)
          (posnat_expt application-judgement "posnat" exponentiation
           nil)
          (int_minus_int_is_int application-judgement "int" 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)
          (int_min application-judgement "{k: int | k <= i AND k <= j}"
           real_defs 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)
          (rat_plus_rat_is_rat application-judgement "rat" rationals
           nil))
         nil))
       (Fminus_TCC1 0
        (Fminus_TCC1-1 nil 3319889173 ("" (subtype-tcc) nil nil)
         ((^ const-decl "real" exponentiation nil)
          (mult_divides2 application-judgement "(divides(m))" divides
           nil)
          (mult_divides1 application-judgement "(divides(n))" divides
           nil)
          (posnat_expt application-judgement "posnat" exponentiation
           nil)
          (int_minus_int_is_int application-judgement "int" 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)
          (int_min application-judgement "{k: int | k <= i AND k <= j}"
           real_defs 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)
          (rat_minus_rat_is_rat application-judgement "rat" rationals
           nil))
         nil))
       (sum_float_commutes 0
        (sum_float_commutes-1 nil 3545039871 ("" (grind) nil nil)
         ((mult_divides2 application-judgement "(divides(m))" divides
           nil)
          (mult_divides1 application-judgement "(divides(n))" divides
           nil)
          (posint_times_posint_is_posint application-judgement "posint"
           integers nil)
          (posnat_expt application-judgement "posnat" exponentiation
           nil)
          (int_minus_int_is_int application-judgement "int" integers
           nil)
          (real_gt_is_strict_total_order name-judgement
           "(strict_total_order?[real])" real_props nil)
          (expt def-decl "real" exponentiation nil)
          (min const-decl "{p: real | p <= m AND p <= n}" real_defs
               nil)
          (^ const-decl "real" exponentiation nil)
          (Fplus const-decl "float" float nil)
          (+ const-decl "float" float nil))
         shostak))
       (mult_float_commutes 0
        (mult_float_commutes-1 nil 3545039902 ("" (grind) nil nil)
         ((Fmult const-decl "float" float nil)
          (* const-decl "float" float nil))
         shostak))
       (FexptCorrect_TCC1 0
        (FexptCorrect_TCC1-1 nil 3545396627 ("" (subtype-tcc) nil nil)
         ((nnrat_exp application-judgement "nnrat" exponentiation nil)
          (posrat_exp application-judgement "posrat" exponentiation
           nil)
          (FtoR const-decl "real" float nil))
         nil))
       (FexptCorrect 0
        (FexptCorrect-1 nil 3545396632
         ("" (skeep)
          (("" (expand "^")
            (("" (expand "Fexpt")
              (("" (expand "FtoR")
                (("" (lemma "mult_expt")
                  (("" (case "n = 0")
                    (("1" (replace -1)
                      (("1" (hide -) (("1" (grind) nil nil)) nil)) nil)
                     ("2" (inst - "n" _ _)
                      (("2" (expand "^" - 1)
                        (("2" (rewrite -1)
                          (("1" (lemma "expt_times")
                            (("1" (inst - "Fexp(f)" "n" "radix")
                              (("1"
                                (replace -1 :dir rl)
                                (("1"
                                  (hide -)
                                  (("1"
                                    (expand "^" + 2)
                                    (("1" (assertnil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (flatten)
                            (("2" (replace -1)
                              (("2"
                                (expand "expt")
                                (("2" (assertnil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ((^ const-decl "real" exponentiation nil)
          (^ const-decl "float" float nil)
          (FtoR const-decl "real" float 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)
          (= const-decl "[T, T -> boolean]" equalities nil)
          (boolean nonempty-type-decl nil booleans nil)
          (number nonempty-type-decl nil numbers nil)
          (rat_times_rat_is_rat application-judgement "rat" rationals
           nil)
          (even_times_int_is_even application-judgement "even_int"
           integers nil)
          (mult_divides1 application-judgement "(divides(n))" divides
           nil)
          (mult_divides2 application-judgement "(divides(m))" divides
           nil)
          (posnat_expt application-judgement "posnat" exponentiation
           nil)
          (posrat_div_posrat_is_posrat application-judgement "posrat"
           rationals nil)
          (real_ge_is_total_order name-judgement "(total_order?[real])"
           real_props nil)
          (rat_expt application-judgement "rat" exponentiation nil)
          (minus_int_is_int application-judgement "int" integers nil)
          (expt def-decl "real" exponentiation nil)
          (posrat_exp application-judgement "posrat" exponentiation
           nil)
          (nnrat_exp application-judgement "nnrat" exponentiation nil)
          (int_expt application-judgement "int" exponentiation nil)
          (nzreal_exp application-judgement "nzreal" exponentiation
           nil)
          (nnrat_times_nnrat_is_nnrat application-judgement
           "nonneg_rat" rationals nil)
          (nnint_times_nnint_is_nnint application-judgement
           "nonneg_int" integers nil)
          (nat_expt application-judgement "nat" exponentiation nil)
          (int_minus_int_is_int application-judgement "int" integers
           nil)
          (expt_times formula-decl nil exponentiation nil)
          (nzreal nonempty-type-eq-decl nil reals nil)
          (OR const-decl "[bool, bool -> bool]" booleans nil)
          (> const-decl "bool" reals nil)
          (above nonempty-type-eq-decl nil integers nil)
          (radix formal-const-decl "above(1)" float nil)
          (f skolem-const-decl "float" float nil)
          (float type-eq-decl nil float nil)
          (/= const-decl "boolean" notequal nil)
          (int_exp application-judgement "int" exponentiation nil)
          (mult_expt formula-decl nil exponentiation nil)
          (Fexpt const-decl "float" float nil))
         nil))
       (sigma_TCC1 0
        (sigma_TCC1-1 nil 3544869888 ("" (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)
          (>= 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)
          (int_minus_int_is_int application-judgement "int" 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))
         nil))
       (sigma_TCC2 0
        (sigma_TCC2-1 nil 3544869888 ("" (termination-tcc) nil nilnil
         nil))
       (FDivInt_TCC1 0
        (FDivInt_TCC1-1 nil 3544783712
         ("" (skeep)
          (("" (typepred "i")
            (("" (case "radix = mod(radix,i) + i * floor(radix / i)")
              (("1" (replace -3)
                (("1" (assert)
                  (("1" (replace -1)
                    (("1" (assert)
                      (("1"
                        (case "FORALL (ii,jj:int): integer_pred(ii*jj)")
                        (("1" (inst - "Fnum(f)" "floor(radix/i)")
                          (("1" (assert)
                            (("1" (hide-all-but (-1 1))
                              (("1" (grind :exclude "floor"nil nil))
                              nil))
                            nil))
                          nil)
                         ("2" (hide-all-but 1) (("2" (grind) nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (expand "mod") (("2" (propax) nil nil)) nil))
              nil))
            nil))
          nil)
         ((radix formal-const-decl "above(1)" float nil)
          (above nonempty-type-eq-decl nil integers nil)
          (> const-decl "bool" reals nil)
          (mod const-decl "{k | abs(k) < abs(j)}" mod nil)
          (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}"
               real_defs nil)
          (- const-decl "[numfield -> numfield]" number_fields nil)
          (numfield nonempty-type-eq-decl nil number_fields nil)
          (AND const-decl "[bool, bool -> bool]" booleans nil)
          (nonneg_real nonempty-type-eq-decl nil real_types nil)
          (>= const-decl "bool" reals nil)
          (< const-decl "bool" reals nil)
          (nonzero_integer nonempty-type-eq-decl nil integers nil)
          (= const-decl "[T, T -> boolean]" equalities nil)
          (nzint nonempty-type-eq-decl nil integers 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)
          (/= const-decl "boolean" notequal 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)
          (mult_divides1 application-judgement "(divides(n))" divides
           nil)
          (mult_divides2 application-judgement "(divides(m))" divides
           nil)
          (float type-eq-decl nil float nil)
          (rat_div_nzrat_is_rat application-judgement "rat" rationals
           nil)
          (rat_times_rat_is_rat application-judgement "rat" rationals
           nil)
          (int_plus_int_is_int application-judgement "int" integers
           nil)
          (nzrat_div_nzrat_is_nzrat application-judgement "nzrat"
           rationals nil)
          (+ const-decl "[numfield, numfield -> numfield]"
             number_fields nil)
          (* const-decl "[numfield, numfield -> numfield]"
             number_fields nil)
          (integer nonempty-type-from-decl nil integers nil)
          (<= const-decl "bool" reals nil)
          (floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil)
          (nznum nonempty-type-eq-decl nil number_fields nil)
          (/ const-decl "[numfield, nznum -> numfield]" number_fields
             nil))
         nil))
       (FDivInt_def 0
        (FDivInt_def-1 nil 3544783715
         ("" (skeep)
          (("" (expand "mod")
            (("" (name "k" "floor(radix/i)")
              (("" (case "k = radix/i")
                (("1" (expand "FDivInt")
                  (("1" (replace -1 :dir rl)
                    (("1" (expand "FtoR")
                      (("1" (lemma "expt_plus")
                        (("1" (inst - "Fexp(f)-1" "1" "radix")
                          (("1" (assertnil nil)) nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (assert)
                  (("2" (replace -1) (("2" (assertnil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ((mult_divides1 application-judgement "(divides(n))" divides
           nil)
          (mult_divides2 application-judgement "(divides(m))" divides
           nil)
          (mod const-decl "{k | abs(k) < abs(j)}" mod nil)
          (expt_plus formula-decl nil exponentiation nil)
          (expt_x1 formula-decl nil exponentiation nil)
          (rat_div_nzrat_is_rat application-judgement "rat" rationals
           nil)
          (rat_times_rat_is_rat application-judgement "rat" rationals
           nil)
          (posint_exp application-judgement "posint" exponentiation
           nil)
          (posrat_times_posrat_is_posrat application-judgement "posrat"
           rationals 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)
          (- const-decl "[numfield, numfield -> numfield]"
             number_fields nil)
          (float type-eq-decl nil float nil)
          (nzreal nonempty-type-eq-decl nil reals nil)
          (int_minus_int_is_int application-judgement "int" integers
           nil)
          (FtoR const-decl "real" float nil)
          (FDivInt const-decl "float" float nil)
          (real_div_nzreal_is_real application-judgement "real" reals
           nil)
          (nzrat_div_nzrat_is_nzrat application-judgement "nzrat"
           rationals nil)
          (number nonempty-type-decl nil numbers nil)
          (boolean nonempty-type-decl nil booleans nil)
          (= const-decl "[T, T -> boolean]" equalities 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)
          (bool nonempty-type-eq-decl nil booleans nil)
          (AND const-decl "[bool, bool -> bool]" booleans nil)
          (<= const-decl "bool" reals nil)
          (< const-decl "bool" reals nil)
          (numfield nonempty-type-eq-decl nil number_fields nil)
          (+ const-decl "[numfield, numfield -> numfield]"
             number_fields nil)
          (floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil)
          (/= const-decl "boolean" notequal nil)
          (nznum nonempty-type-eq-decl nil number_fields nil)
          (/ const-decl "[numfield, nznum -> numfield]" number_fields
             nil)
          (int nonempty-type-eq-decl nil integers nil)
          (> const-decl "bool" reals nil)
          (above nonempty-type-eq-decl nil integers nil)
          (radix formal-const-decl "above(1)" float nil)
          (nzint nonempty-type-eq-decl nil integers nil))
         shostak))
       (hathatln_TCC1 0
        (hathatln_TCC1-1 nil 3318954543
         ("" (grind-reals)
          (("" (wrap-formula -1 "exp")
            (("1" (rewrite "exp_ln" -1) (("1" (grind-reals) nil nil))
              nil)
             ("2" (grind-reals) nil nil))
            nil))
          nil)
         ((number nonempty-type-decl nil numbers nil)
          (= const-decl "[T, T -> boolean]" equalities 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)
          (ln const-decl "real" ln_exp "lnexp_fnd/")
          (exp const-decl "{py | x = ln(py)}" ln_exp "lnexp_fnd/")
          (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)
          (above nonempty-type-eq-decl nil integers nil)
          (radix formal-const-decl "above(1)" float nil)
          (TRUE const-decl "bool" booleans nil)
          (id const-decl "(bijective?[T, T])" identity nil)
          (bijective? const-decl "bool" functions nil)
          (bool nonempty-type-eq-decl nil booleans nil)
          (boolean nonempty-type-decl nil booleans nil)
          (exp_0 formula-decl nil ln_exp "lnexp_fnd/")
          (exp_ln formula-decl nil ln_exp "lnexp_fnd/"))
         nil))
       (hathatln_TCC2 0
        (hathatln_TCC2-1 nil 3318954543 ("" (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)
          (>= 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)
          (/= const-decl "boolean" notequal nil)
          (ln const-decl "real" ln_exp "lnexp_fnd/")
          (real_div_nzreal_is_real application-judgement "real" reals
           nil))
         nil))
       (hathatln 0
        (hathatln-1 nil 3318954554
         ("" (skeep)
          (("" (expand "^^")
            (("" (case "radix=0")
              (("1" (assertnil nil)
               ("2" (assert)
                (("2"
                  (case-replace
                   "-(ln(r) / ln(radix)) * ln(radix) = -ln(r)")
                  (("1" (hide -1)
                    (("1" (rewrite "exp_neg")
                      (("1" (rewrite "exp_ln"nil nil)) nil))
                    nil)
                   ("2" (assertnil nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ((real_div_nzreal_is_real application-judgement "real" reals
           nil)
          (minus_real_is_real application-judgement "real" reals nil)
          (^^ const-decl "nnreal" expt "lnexp_fnd/")
          (posreal_div_posreal_is_posreal application-judgement
           "posreal" real_types nil)
          (real_times_real_is_real application-judgement "real" reals
           nil)
          (exp_ln formula-decl nil ln_exp "lnexp_fnd/")
          (exp_neg formula-decl nil ln_exp "lnexp_fnd/")
          (ln const-decl "real" ln_exp "lnexp_fnd/")
          (posreal nonempty-type-eq-decl nil real_types nil)
          (nonneg_real nonempty-type-eq-decl nil real_types nil)
          (>= const-decl "bool" reals nil)
          (/ const-decl "[numfield, nznum -> numfield]" number_fields
             nil)
          (nznum nonempty-type-eq-decl nil number_fields nil)
          (/= const-decl "boolean" notequal nil)
          (- const-decl "[numfield -> numfield]" number_fields nil)
          (* const-decl "[numfield, numfield -> numfield]"
             number_fields nil)
          (numfield nonempty-type-eq-decl nil number_fields nil)
          (number nonempty-type-decl nil numbers nil)
          (boolean nonempty-type-decl nil booleans nil)
          (= const-decl "[T, T -> boolean]" equalities 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)
          (bool nonempty-type-eq-decl nil booleans nil)
          (> const-decl "bool" reals nil)
          (above nonempty-type-eq-decl nil integers nil)
          (radix formal-const-decl "above(1)" float nil))
         shostak))
       (hathat_int_TCC1 0
        (hathat_int_TCC1-1 nil 3319195930 ("" (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)
          (int nonempty-type-eq-decl nil integers nil)
          (/= const-decl "boolean" notequal nil))
         nil))
       (hathat_int_TCC2 0
        (hathat_int_TCC2-1 nil 3545651010 ("" (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)
          (int nonempty-type-eq-decl nil integers nil)
          (/= const-decl "boolean" notequal nil))
         nil))
       (hathat_int 0
        (hathat_int-1 nil 3319197088
         ("" (skeep)
          (("" (expand "^")
            (("" (case "e1 >= 0")
              (("1" (grind-reals)
                (("1" (rewrite "hathat_nat")
                  (("1" (expand "^") (("1" (propax) nil nil)) nil))
                  nil))
                nil)
               ("2" (grind-reals)
                (("2" (lemma "hathat_diff")
                  (("2" (inst -1 "radix" "-e1" "0")
                    (("2" (case-replace "0--e1=e1")
                      (("1" (rewrite -2)
                        (("1" (rewrite "hathat_nat")
                          (("1" (expand "^")
                            (("1" (grind-reals) nil nil)) nil))
                          nil))
                        nil)
                       ("2" (hide -1 2 3) (("2" (assertnil nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ((^ const-decl "real" exponentiation nil)
          (div_cancel4 formula-decl nil real_props nil)
          (posrat_div_posrat_is_posrat application-judgement "posrat"
           rationals nil)
          (minus_int_is_int application-judgement "int" integers nil)
          (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
           real_types nil)
          (numfield nonempty-type-eq-decl nil number_fields nil)
          (- const-decl "[numfield -> numfield]" number_fields nil)
          (hathat_to_0 formula-decl nil expt "lnexp_fnd/")
          (real_div_nzreal_is_real application-judgement "real" reals
           nil)
          (nnreal_div_posreal_is_nnreal application-judgement "nnreal"
           real_types nil)
          (posrat_times_posrat_is_posrat application-judgement "posrat"
           rationals nil)
          (div_cancel2 formula-decl nil real_props nil)
          (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
           real_types nil)
          (int_minus_int_is_int application-judgement "int" integers
           nil)
          (= const-decl "[T, T -> boolean]" equalities nil)
          (- const-decl "[numfield, numfield -> numfield]"
             number_fields nil)
          (hathat_diff formula-decl nil expt "lnexp_fnd/")
          (real_ge_is_total_order name-judgement "(total_order?[real])"
           real_props nil)
          (posnat_expt application-judgement "posnat" exponentiation
           nil)
          (nnrat_exp application-judgement "nnrat" exponentiation nil)
          (posrat_exp application-judgement "posrat" exponentiation
           nil)
          (nat nonempty-type-eq-decl nil naturalnumbers nil)
          (radix formal-const-decl "above(1)" float nil)
          (above nonempty-type-eq-decl nil integers 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)
          (hathat_nat formula-decl nil expt "lnexp_fnd/")
          (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)
          (bool nonempty-type-eq-decl nil booleans 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))
         shostak))
       (Fsucc_TCC1 0
        (Fsucc_TCC1-1 nil 3321636413
         ("" (skeep)
          (("" (lemma "radix_div_vNum") (("" (inst?) nil nil)) nil))
          nil)
         ((radix_div_vNum formula-decl nil float nil)
          (nat nonempty-type-eq-decl nil naturalnumbers nil)
          (above nonempty-type-eq-decl nil integers nil)
          (Format type-eq-decl nil float nil))
         nil))
       (Fpred_TCC1 0
        (Fpred_TCC1-1 nil 3319211903
         ("" (skeep)
          (("" (case-replace "-vNum(b) / radix = -(vNum(b)/radix)")
            (("1" (hide -1)
              (("1" (lemma "integers.closed_neg")
                (("1" (inst?)
                  (("1" (hide 2)
                    (("1" (lemma "radix_div_vNum")
                      (("1" (inst -1 "b"nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (hide 2) (("2" (assertnil nil)) nil))
            nil))
          nil)
         ((nzrat_div_nzrat_is_nzrat application-judgement "nzrat"
           rationals nil)
          (minus_nzrat_is_nzrat application-judgement "nzrat" rationals
           nil)
          (number nonempty-type-decl nil numbers nil)
          (boolean nonempty-type-decl nil booleans nil)
          (= const-decl "[T, T -> boolean]" equalities 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)
          (/= 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]" number_fields nil)
          (nat nonempty-type-eq-decl nil naturalnumbers nil)
          (above nonempty-type-eq-decl nil integers nil)
          (Format type-eq-decl nil float 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)
          (bool nonempty-type-eq-decl nil booleans nil)
          (>= const-decl "bool" reals nil)
          (nonneg_int nonempty-type-eq-decl nil integers nil)
          (> const-decl "bool" reals nil)
          (posnat nonempty-type-eq-decl nil integers nil)
          (vNum const-decl "posnat" float nil)
          (radix formal-const-decl "above(1)" float nil)
          (int_minus_int_is_int application-judgement "int" integers
           nil)
          (minus_nzint_is_nzint application-judgement "nzint" integers
           nil)
          (closed_neg formula-decl nil integers nil)
          (radix_div_vNum formula-decl nil float nil)
          (b skolem-const-decl "Format" float nil)
          (posrat_div_posrat_is_posrat application-judgement "posrat"
           rationals nil))
         nil))
       (Fnormalize_TCC1 0
        (Fnormalize_TCC1-1 nil 3318871237 ("" (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)
          (nat nonempty-type-eq-decl nil naturalnumbers nil)
          (above nonempty-type-eq-decl nil integers nil)
          (Format type-eq-decl nil float nil)
          (int nonempty-type-eq-decl nil integers nil)
          (float type-eq-decl nil float nil)
          (Fbounded? const-decl "bool" float nil)
          (^ const-decl "real" exponentiation 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)
          (real_le_is_total_order name-judgement "(total_order?[real])"
           real_props nil)
          (minus_int_is_int application-judgement "int" integers nil)
          (int_minus_int_is_int application-judgement "int" integers
           nil)
          (posnat_expt application-judgement "posnat" exponentiation
           nil)
          (vNum const-decl "posnat" float nil)
          (int_abs_is_nonneg application-judgement
           "{j: nonneg_int | j >= i}" real_defs nil)
          (posint_exp application-judgement "posint" exponentiation
           nil))
         nil))
       (Fnormalize_TCC2 0
        (Fnormalize_TCC2-1 nil 3318871237 ("" (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)
          (nat nonempty-type-eq-decl nil naturalnumbers nil)
          (above nonempty-type-eq-decl nil integers nil)
          (Format type-eq-decl nil float nil)
          (int nonempty-type-eq-decl nil integers nil)
          (float type-eq-decl nil float nil)
          (^ const-decl "real" exponentiation nil)
          (real_lt_is_strict_total_order name-judgement
           "(strict_total_order?[real])" real_props nil)
          (int_abs_is_nonneg application-judgement
           "{j: nonneg_int | j >= i}" real_defs nil)
          (posint_exp application-judgement "posint" exponentiation
           nil)
          (real_ge_is_total_order name-judgement "(total_order?[real])"
           real_props nil)
          (real_le_is_total_order name-judgement "(total_order?[real])"
           real_props nil)
          (minus_int_is_int application-judgement "int" integers nil)
          (posnat_expt application-judgement "posnat" exponentiation
           nil)
          (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}"
               real_defs nil)
          (vNum const-decl "posnat" float nil)
          (Fbounded? const-decl "bool" float nil)
          (Fnormal? const-decl "bool" float nil)
          (Fsubnormal? const-decl "bool" float nil)
          (Fcanonic? const-decl "bool" float nil)
          (FtoR const-decl "real" float nil)
          (nnrat_exp application-judgement "nnrat" exponentiation nil)
          (posrat_exp application-judgement "posrat" exponentiation
           nil))
         nil))
       (Fnormalize_TCC3 0
        (Fnormalize_TCC3-1 nil 3318871237 ("" (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)
          (nat nonempty-type-eq-decl nil naturalnumbers nil)
          (above nonempty-type-eq-decl nil integers nil)
          (Format type-eq-decl nil float nil)
          (int nonempty-type-eq-decl nil integers nil)
          (float type-eq-decl nil float nil)
          (Fbounded? const-decl "bool" float nil)
          (^ const-decl "real" exponentiation nil)
          (posnat_expt application-judgement "posnat" exponentiation
           nil)
          (minus_int_is_int application-judgement "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)
          (posint_exp application-judgement "posint" exponentiation
           nil)
          (int_abs_is_nonneg application-judgement
           "{j: nonneg_int | j >= i}" real_defs nil)
          (real_lt_is_strict_total_order name-judgement
           "(strict_total_order?[real])" real_props nil)
          (vNum const-decl "posnat" float nil)
          (Fnormal? const-decl "bool" float nil)
          (Fsubnormal? const-decl "bool" float nil)
          (Fcanonic? const-decl "bool" float nil)
          (mult_divides1 application-judgement "(divides(n))" divides
           nil)
          (mult_divides2 application-judgement "(divides(m))" divides
           nil))
         nil))
       (Fnormalize_TCC4 0
        (Fnormalize_TCC4-1 nil 3318871237 ("" (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)
          (nat nonempty-type-eq-decl nil naturalnumbers nil)
          (above nonempty-type-eq-decl nil integers nil)
          (Format type-eq-decl nil float nil)
          (int nonempty-type-eq-decl nil integers nil)
          (float type-eq-decl nil float nil)
          (posnat_expt application-judgement "posnat" exponentiation
           nil)
          (minus_int_is_int application-judgement "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)
          (posint_exp application-judgement "posint" exponentiation
           nil)
          (int_abs_is_nonneg application-judgement
           "{j: nonneg_int | j >= i}" real_defs nil)
          (real_lt_is_strict_total_order name-judgement
           "(strict_total_order?[real])" real_props nil)
          (^ const-decl "real" exponentiation nil)
          (vNum const-decl "posnat" float nil)
          (Fbounded? const-decl "bool" float nil)
          (mult_divides1 application-judgement "(divides(n))" divides
           nil)
          (mult_divides2 application-judgement "(divides(m))" divides
           nil))
         nil))
       (Fnormalize_TCC5 0
        (Fnormalize_TCC5-1 nil 3318871660
         ("" (skosimp)
          (("" (grind-reals)
            (("" (expand "abs" 4 2)
              (("" (wrap-formula 2 "abs")
                (("" (expand "abs" 1 2)
                  (("" (cancel-by 4 "abs(Fnum(f!1))")
                    (("" (hide-all-but (-1 3)) (("" (grind) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ((both_sides_minus_lt2 formula-decl nil real_props nil)
          (abs_mult formula-decl nil real_props nil)
          (minus_int_is_int application-judgement "int" integers nil)
          (real_ge_is_total_order name-judgement "(total_order?[real])"
           real_props nil)
          (int_abs_is_nonneg application-judgement
           "{j: nonneg_int | j >= i}" real_defs nil)
          (nnint_times_nnint_is_nnint application-judgement
           "nonneg_int" integers nil)
          (nzint_abs_is_pos application-judgement
           "{j: posint | j >= i}" real_defs nil)
          (real_lt_is_strict_total_order name-judgement
           "(strict_total_order?[real])" real_props nil)
          (int_minus_int_is_int application-judgement "int" integers
           nil)
          (real_le_is_total_order name-judgement "(total_order?[real])"
           real_props 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)
          (AND const-decl "[bool, bool -> bool]" booleans nil)
          (numfield nonempty-type-eq-decl nil number_fields nil)
          (- const-decl "[numfield -> numfield]" number_fields nil)
          (* const-decl "[numfield, numfield -> numfield]"
             number_fields 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)
          (radix formal-const-decl "above(1)" float nil)
          (float type-eq-decl nil float nil)
          (nat nonempty-type-eq-decl nil naturalnumbers nil)
          (Format type-eq-decl nil float nil)
          (Fbounded? const-decl "bool" float nil)
          (nonneg_int nonempty-type-eq-decl nil integers nil)
          (posnat nonempty-type-eq-decl nil integers nil)
          (vNum const-decl "posnat" float nil)
          (boolean nonempty-type-decl nil booleans nil)
          (bool nonempty-type-eq-decl nil booleans nil)
          (bijective? const-decl "bool" functions nil)
          (id const-decl "(bijective?[T, T])" identity nil)
          (TRUE const-decl "bool" booleans nil)
          (abs_abs formula-decl nil real_props nil)
          (div_cancel1 formula-decl nil real_props nil)
          (rat_times_rat_is_rat application-judgement "rat" rationals
           nil)
          (< const-decl "bool" reals nil)
          (pos_div_ge formula-decl nil real_props nil)
          (real_gt_is_strict_total_order name-judgement
           "(strict_total_order?[real])" real_props nil)
          (/= const-decl "boolean" notequal nil)
          (b!1 skolem-const-decl "Format" float nil)
          (f!1 skolem-const-decl "(Fbounded?(b!1))" float nil)
          (CBD_1 skolem-const-decl
           "{n: nonneg_real | n >= Fnum(f!1) AND n >= -Fnum(f!1)}"
           float nil)
          (nznum nonempty-type-eq-decl nil number_fields nil)
          (/ const-decl "[numfield, nznum -> numfield]" number_fields
             nil)
          (both_sides_times_pos_ge1_imp formula-decl nil
           extra_real_props nil)
          (nzrat_div_nzrat_is_nzrat application-judgement "nzrat"
           rationals nil)
          (= const-decl "[T, T -> boolean]" equalities nil)
          (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}"
               real_defs nil)
          (mult_divides2 application-judgement "(divides(m))" divides
           nil)
          (mult_divides1 application-judgement "(divides(n))" divides
           nil))
         nil))
       (Fnormalize_TCC6 0
        (Fnormalize_TCC6-1 nil 3319287157
         ("" (skosimp)
          (("" (split)
            (("1"
              (typepred
               "v!1(b!1)((# Fnum := radix * Fnum(f!1), Fexp := Fexp(f!1) - 1 #))")
              (("1" (replaces -2)
                (("1" (expand "FtoR")
                  (("1" (rewrite "expt_div" :dir rl)
                    (("1" (rewrite "expt_x1") (("1" (assertnil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2"
              (typepred
               "v!1(b!1)((# Fnum := radix * Fnum(f!1), Fexp := Fexp(f!1) - 1 #))")
              (("2" (assertnil nil)) nil))
            nil))
          nil)
         ((nzreal nonempty-type-eq-decl nil reals nil)
          (/= const-decl "boolean" notequal nil)
          (expt_div formula-decl nil exponentiation nil)
          (posrat_exp application-judgement "posrat" exponentiation
           nil)
          (rat_times_rat_is_rat application-judgement "rat" rationals
           nil)
          (posint_exp application-judgement "posint" exponentiation
           nil)
          (nnrat_exp application-judgement "nnrat" exponentiation nil)
          (posrat_div_posrat_is_posrat application-judgement "posrat"
           rationals nil)
          (expt_x1 formula-decl nil exponentiation nil)
          (real_le_is_total_order name-judgement "(total_order?[real])"
           real_props nil)
          (int_minus_int_is_int application-judgement "int" integers
           nil)
          (boolean nonempty-type-decl nil booleans nil)
          (bool nonempty-type-eq-decl nil booleans nil)
          (NOT const-decl "[bool -> bool]" booleans nil)
          (nat nonempty-type-eq-decl nil naturalnumbers nil)
          (above nonempty-type-eq-decl nil integers nil)
          (Format type-eq-decl nil float nil)
          (int nonempty-type-eq-decl nil integers nil)
          (float type-eq-decl nil float nil)
          (Fcanonic? const-decl "bool" float nil)
          (Fbounded? const-decl "bool" float 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)
          (numfield nonempty-type-eq-decl nil number_fields nil)
          (- const-decl "[numfield, numfield -> numfield]"
             number_fields 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)
          (>= const-decl "bool" reals nil)
          (nonneg_int nonempty-type-eq-decl nil integers nil)
          (> const-decl "bool" reals nil)
          (posnat nonempty-type-eq-decl nil integers nil)
          (vNum const-decl "posnat" float nil)
          (nonneg_real nonempty-type-eq-decl nil real_types nil)
          (AND const-decl "[bool, bool -> bool]" booleans nil)
          (- const-decl "[numfield -> numfield]" number_fields nil)
          (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}"
               real_defs nil)
          (= const-decl "[T, T -> boolean]" equalities nil)
          (FtoR const-decl "real" float nil)
          (<= const-decl "bool" reals nil)
          (* const-decl "[numfield, numfield -> numfield]"
             number_fields nil)
          (radix formal-const-decl "above(1)" float nil)
          (mult_divides2 application-judgement "(divides(m))" divides
           nil)
          (mult_divides1 application-judgement "(divides(n))" divides
           nil)
          (int_abs_is_nonneg application-judgement
           "{j: nonneg_int | j >= i}" real_defs nil))
         nil))
       (Fulp_TCC1 0
        (Fulp_TCC1-1 nil 3318887371 ("" (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)
          (nat nonempty-type-eq-decl nil naturalnumbers nil)
          (above nonempty-type-eq-decl nil integers nil)
          (Format type-eq-decl nil float nil)
          (int nonempty-type-eq-decl nil integers nil)
          (float type-eq-decl nil float nil)
          (Fbounded? const-decl "bool" float nil)
          (vNum const-decl "posnat" float nil)
          (minus_int_is_int application-judgement "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)
          (posint_exp application-judgement "posint" exponentiation
           nil)
          (int_abs_is_nonneg application-judgement
           "{j: nonneg_int | j >= i}" real_defs nil)
          (real_lt_is_strict_total_order name-judgement
           "(strict_total_order?[real])" real_props nil)
          (/= const-decl "boolean" notequal nil))
         nil))
       (FcanonicOpp 0
        (FcanonicOpp-1 nil 3319221457
         ("" (skeep)
          (("" (split)
            (("1" (skosimp*)
              (("1" (expand "Fcanonic?")
                (("1" (split)
                  (("1" (case "Fnormal?(b)(Fopp(f))")
                    (("1" (assertnil nil)
                     ("2" (hide 2)
                      (("2" (expand"Fnormal?" "Fbounded?" "Fopp")
                        (("2" (flatten)
                          (("2" (split)
                            (("1"
                              (case-replace
                               "abs(-(Fnum(f)))=abs(Fnum(f))")
                              (("1"
                                (hide -1 -2 -3 2)
                                (("1"
                                  (expand "abs")
                                  (("1" (grind-reals) nil nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (propax) nil nil)
                             ("3"
                              (case-replace
                               "abs(radix * -(Fnum(f)))=abs(radix * Fnum(f))")
                              (("3"
                                (hide -1 -2 -3 2)
                                (("3"
                                  (expand "abs")
                                  (("3"
                                    (grind-reals)
                                    (("1"
                                      (case "-(radix * (Fnum(f))) > 0")
                                      (("1" (grind-reals) nil nil)
                                       ("2"
                                        (hide -1)
                                        (("2"
                                          (cancel-by 1 "radix")
                                          nil
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (flip-ineq 2)
                                      (("2"
                                        (hide 2)
                                        (("2"
                                          (cancel-by 1 "radix")
                                          nil
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (case "Fsubnormal?(b)(Fopp(f))")
                    (("1" (assertnil nil)
                     ("2" (hide 2)
                      (("2" (expand"Fopp" "Fsubnormal?" "Fbounded?")
                        (("2" (flatten)
                          (("2" (split)
                            (("1"
                              (case-replace
                               "abs(-(Fnum(f)))=abs(Fnum(f))")
                              (("1"
                                (hide -1 -2 -3 -4 2)
                                (("1"
                                  (expand "abs")
                                  (("1" (grind-reals) nil nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (propax) nil nil)
                             ("3" (propax) nil nil)
                             ("4"
                              (case-replace
                               "abs(radix * -(Fnum(f)))=abs(radix * Fnum(f))")
                              (("4"
                                (hide -1 -2 -3 -4 2)
                                (("4"
                                  (expand "abs")
                                  (("4"
                                    (grind-reals)
                                    (("1"
                                      (flip-ineq -1)
                                      (("1"
                                        (cancel-by 1 "radix")
                                        nil
                                        nil))
                                      nil)
                                     ("2"
                                      (flip-ineq 2)
                                      (("2"
                                        (hide 2)
                                        (("2"
                                          (cancel-by 1 "radix")
                                          nil
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (skosimp*)
              (("2" (expand "Fcanonic?")
                (("2" (split)
                  (("1" (case "Fnormal?(b)(f)")
                    (("1" (assertnil nil)
                     ("2" (hide 2)
                      (("2" (expand"Fnormal?" "Fopp" "Fbounded?")
                        (("2" (flatten)
                          (("2" (split)
                            (("1"
                              (case-replace
                               "abs(Fnum(f))=abs(-(Fnum(f)))")
                              (("1"
                                (hide -1 -2 -3 2)
                                (("1"
                                  (expand "abs")
                                  (("1" (grind-reals) nil nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (propax) nil nil)
                             ("3"
                              (case-replace
                               "abs(radix * (Fnum(f)))=abs(radix * -(Fnum(f)))")
                              (("3"
                                (hide -1 -2 -3 2)
                                (("3"
                                  (expand "abs")
                                  (("3"
                                    (grind-reals)
                                    (("1"
                                      (flip-ineq -2)
                                      (("1"
                                        (cancel-by 1 "radix")
                                        nil
                                        nil))
                                      nil)
                                     ("2"
                                      (flip-ineq 1)
                                      (("2"
                                        (cancel-by 1 "radix")
                                        nil
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (case " Fsubnormal?(b)(f)")
                    (("1" (assertnil nil)
                     ("2" (hide 2)
                      (("2" (expand"Fsubnormal?" "Fopp" "Fbounded?")
                        (("2" (flatten)
                          (("2" (split)
                            (("1"
                              (case-replace
                               "abs(Fnum(f))=abs(-(Fnum(f)))")
                              (("1"
                                (hide -1 -2 -3 -4 2)
                                (("1"
                                  (expand "abs")
                                  (("1" (grind-reals) nil nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (propax) nil nil)
                             ("3" (propax) nil nil)
                             ("4"
                              (case-replace
                               "abs(radix * (Fnum(f)))=abs(radix * -(Fnum(f)))")
                              (("4"
                                (hide -1 -2 -3 -4 2)
                                (("4"
                                  (expand "abs")
                                  (("4"
                                    (grind-reals)
                                    (("1"
                                      (flip-ineq -2)
                                      (("1"
                                        (cancel-by 1 "radix")
                                        nil
                                        nil))
                                      nil)
                                     ("2"
                                      (flip-ineq 1)
                                      (("2"
                                        (cancel-by 1 "radix")
                                        nil
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ((Fcanonic? const-decl "bool" float nil)
--> --------------------

--> maximum size reached

--> --------------------

¤ Dauer der Verarbeitung: 0.102 Sekunden  (vorverarbeitet)  ¤





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