Quellcode-Bibliothek

^© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: max_below.pvs 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: 0.10 Sekunden (vorverarbeitet) ¤

Druckansicht unsichere Verbindung
Druckansicht sprechenden Kalenders
in der Quellcodebibliothek suchen

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.