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Datei: factorial.prf Sprache: Lisp

Original von: PVS^©

(factorial
(factorial_TCC1 0
  (factorial_TCC1-1 nil 3298303363 ("" (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_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   nil))
(factorial_TCC2 0
  (factorial_TCC2-1 nil 3298303363 ("" (termination-tcc) nil nil) nil
   nil))
(factorial_TCC3 0
  (factorial_TCC3-1 nil 3298303363
   ("" (skosimp*)
    (("" (typepred "v!1(n!1 - 1)")
      (("1" (mult-cases 2) nil nil) ("2" (assert) nil nil)) nil))
    nil)
   ((- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (< const-decl "bool" reals 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)
    (> 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)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (pos_times_gt formula-decl nil real_props nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
(factorial_0 0
  (factorial_0-1 nil 3298303363 ("" (grind) nil nil)
   ((factorial def-decl "posnat" factorial nil)) shostak))
(factorial_1 0
  (factorial_1-1 nil 3298303369 ("" (grind) nil 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)
    (factorial def-decl "posnat" factorial nil))
   shostak))
(factorial_2 0
  (factorial_2-1 nil 3298303372 ("" (grind) nil nil)
   ((posint_times_posint_is_posint application-judgement "posint"
     integers 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)
    (factorial def-decl "posnat" factorial nil))
   shostak))
(factorial_3 0
  (factorial_3-1 nil 3298303376 ("" (grind) nil 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)
    (even_times_int_is_even application-judgement "even_int" integers
     nil)
    (factorial def-decl "posnat" factorial nil))
   shostak))
(factorial_def 0
  (factorial_def-1 nil 3298303379
   ("" (skosimp*) (("" (grind) nil nil)) nil)
   ((mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (factorial def-decl "posnat" factorial nil))
   shostak))
(factorial_n_TCC1 0
  (factorial_n_TCC1-1 nil 3298303461
   ("" (skosimp*) (("" (assert) nil nil)) nil)
   ((int_minus_int_is_int application-judgement "int" integers 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))
   shostak))
(factorial_n 0
  (factorial_n-1 nil 3298303451 ("" (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)
    (factorial def-decl "posnat" factorial nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_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))
   shostak))
(factorial_plus1 0
  (factorial_plus1-1 nil 3298372726
   ("" (skosimp*)
    (("" (expand "factorial" 1 1) (("" (propax) nil nil)) nil)) nil)
   ((factorial def-decl "posnat" factorial nil)) shostak))
(factorial_gt_TCC1 0
  (factorial_gt_TCC1-1 nil 3301995131
   ("" (skosimp*) (("" (assert) nil nil)) nil)
   ((int_minus_int_is_int application-judgement "int" integers 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))
   shostak))
(factorial_gt 0
  (factorial_gt-1 nil 3301994550
   ("" (induct "n")
    (("1" (skosimp*) (("1" (assert) nil nil)) nil)
     ("2" (skosimp*)
      (("2"
        (case-replace "k!1 ^ (j!1 + 1 - k!1) = k!1*k!1 ^ (j!1 - k!1)")
        (("1" (hide -1)
          (("1" (expand "factorial" 1 1)
            (("1" (inst?)
              (("1" (assert)
                (("1" (case-replace "j!1 = k!1")
                  (("1" (assert)
                    (("1" (expand "^")
                      (("1" (expand "expt") (("1" (assert) nil nil))
                        nil))
                      nil))
                    nil)
                   ("2" (assert)
                    (("2" (mult-ineq -1 -2) (("2" (assert) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (hide 2)
          (("2" (expand "^")
            (("2" (lift-if)
              (("2" (ground)
                (("2" (expand "expt" 1 1) (("2" (propax) nil nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("3" (assert) nil nil) ("4" (assert) nil nil))
        nil))
      nil)
     ("3" (skosimp*) (("3" (assert) nil nil)) nil))
    nil)
   ((rat_times_rat_is_rat application-judgement "rat" rationals nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (nat_expt application-judgement "nat" exponentiation nil)
    (expt def-decl "real" exponentiation nil)
    (nat_exp application-judgement "nat" exponentiation nil)
    (posint_times_posint_is_posint application-judgement "posint"
     integers nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (gt_times_gt_any1 formula-decl nil extra_real_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (nnrat_exp application-judgement "nnrat" exponentiation nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields 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)
    (nat_induction formula-decl nil naturalnumbers nil)
    (^ const-decl "real" exponentiation nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (factorial def-decl "posnat" factorial nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (pred type-eq-decl nil defined_types 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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (> const-decl "bool" reals nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nnrat_times_nnrat_is_nnrat application-judgement "nonneg_rat"
     rationals nil))
   shostak))
(factorial_ge_TCC1 0
  (factorial_ge_TCC1-1 nil 3302012245
   ("" (skosimp*) (("" (assert) nil nil)) nil)
   ((int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
(factorial_ge 0
  (factorial_ge-1 nil 3302012207
   ("" (skosimp*)
    (("" (lemma "factorial_gt")
      (("" (inst?)
        (("" (assert)
          (("" (case-replace "n!1 = k!1")
            (("1" (assert)
              (("1" (expand "^")
                (("1" (expand "expt") (("1" (assert) nil nil)) nil))
                nil))
              nil)
             ("2" (assert) nil nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((factorial_gt formula-decl nil factorial nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nnrat_exp application-judgement "nnrat" exponentiation nil)
    (nnrat_times_nnrat_is_nnrat application-judgement "nonneg_rat"
     rationals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nat_exp application-judgement "nat" exponentiation nil)
    (expt def-decl "real" 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)
    (^ const-decl "real" exponentiation nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (= const-decl "[T, T -> boolean]" equalities 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))
   shostak))
(factorial_incr 0
  (factorial_incr-1 nil 3301995193
   ("" (induct "n")
    (("1" (skosimp*) (("1" (assert) nil nil)) nil)
     ("2" (skosimp*)
      (("2" (rewrite "factorial_plus1")
        (("2" (case-replace "j!1 = 0")
          (("1" (assert)
            (("1" (hide -1 -2)
              (("1" (case-replace "k!1 = 0")
                (("1" (grind) nil nil)
                 ("2" (case-replace "k!1 = 1")
                  (("1" (grind) nil nil) ("2" (assert) nil nil)) nil))
                nil))
              nil))
            nil)
           ("2" (inst?)
            (("2" (split -1)
              (("1" (assert) nil nil)
               ("2" (assert)
                (("2" (case-replace "k!1 = j!1+1")
                  (("1" (assert)
                    (("1" (rewrite "factorial_plus1")
                      (("1" (assert) nil nil)) nil))
                    nil)
                   ("2" (assert) nil nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((= const-decl "[T, T -> boolean]" equalities nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (even_plus_odd_is_odd application-judgement "odd_int" integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (int_times_even_is_even application-judgement "even_int" integers
     nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (even_minus_odd_is_odd application-judgement "odd_int" integers
     nil)
    (odd_plus_odd_is_even application-judgement "even_int" integers
     nil)
    (odd_minus_odd_is_even application-judgement "even_int" integers
     nil)
    (int_plus_int_is_int application-judgement "int" integers 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)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (factorial_plus1 formula-decl nil factorial nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (factorial def-decl "posnat" factorial nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (<= const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pred type-eq-decl nil defined_types 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))
   shostak))
(factorial_strict_incr 0
  (factorial_strict_incr-1 nil 3301996095
   ("" (induct "n")
    (("1" (skosimp*) (("1" (assert) nil nil)) nil)
     ("2" (skosimp*)
      (("2" (rewrite "factorial_plus1")
        (("2" (case-replace "j!1 = 0")
          (("1" (assert) nil nil)
           ("2" (inst?)
            (("2" (case-replace "k!1 = j!1")
              (("1" (assert)
                (("1" (typepred "factorial(j!1)")
                  (("1" (mult-by -1 "j!1") (("1" (assert) nil nil))
                    nil))
                  nil))
                nil)
               ("2" (assert) nil nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((= const-decl "[T, T -> boolean]" equalities nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (even_plus_odd_is_odd application-judgement "odd_int" integers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (even_times_int_is_even application-judgement "even_int" integers
     nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (both_sides_times_pos_gt1 formula-decl nil real_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers 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)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (factorial_plus1 formula-decl nil factorial nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (factorial def-decl "posnat" factorial nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (< const-decl "bool" reals nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pred type-eq-decl nil defined_types 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))
   shostak))
(factorial_lt_n2n_TCC1 0
  (factorial_lt_n2n_TCC1-1 nil 3322223789 ("" (subtype-tcc) nil nil)
   ((/= const-decl "boolean" notequal nil)) nil))
(factorial_lt_n2n 0
  (factorial_lt_n2n-1 nil 3322223810
   ("" (induct "n")
    (("1" (expand "^")
      (("1" (expand "expt")
        (("1" (expand "factorial") (("1" (assert) nil nil)) nil)) nil))
      nil)
     ("2" (skosimp)
      (("2" (expand "factorial" 1)
        (("2" (rewrite "expt_plus" 1)
          (("2" (rewrite "expt_x1")
            (("2"
              (lemma "both_sides_times_pos_le1"
               ("pz" "1+j!1" "x" "factorial(j!1)" "y" "(1 + j!1)^j!1"))
              (("2" (replace -1 1)
                (("2" (hide -1)
                  (("2" (typepred "j!1")
                    (("2" (expand ">=" -1)
                      (("2" (expand "<=" -1)
                        (("2" (split)
                          (("1"
                            (lemma "both_sides_expt_pos_le"
                             ("px" "j!1" "py" "1+j!1" "pm" "j!1"))
                            (("1" (assert) nil nil)
                             ("2" (assert) nil nil))
                            nil)
                           ("2" (replace -1 * rl)
                            (("2" (expand "factorial")
                              (("2"
                                (expand "^")
                                (("2"
                                  (expand "expt")
                                  (("2" (propax) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (nzreal nonempty-type-eq-decl nil reals nil)
    (expt_plus formula-decl nil exponentiation nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (posint_exp application-judgement "posint" exponentiation 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)
    (both_sides_times_pos_le1 formula-decl nil real_props nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nat_exp application-judgement "nat" exponentiation nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (both_sides_expt_pos_le formula-decl nil exponentiation nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (expt_x1 formula-decl nil exponentiation nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (expt def-decl "real" exponentiation nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (^ const-decl "real" exponentiation nil)
    (/= const-decl "boolean" notequal nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (factorial def-decl "posnat" factorial nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (<= const-decl "bool" reals nil)
    (pred type-eq-decl nil defined_types 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))
   nil)))

¤ Dauer der Verarbeitung: 0.8 Sekunden (vorverarbeitet) ¤

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