Quellcode-Bibliothek

^© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: mod_nat.prf Sprache: Lisp

Original von: PVS^©

(mod_nat
(nmod_TCC1 0
  (nmod_TCC1-1 nil 3507028517
   ("" (skosimp*)
    (("" (assert)
      (("" (lemma "div_smaller")
        (("" (inst?)
          (("" (assert) (("" (rewrite "div_rem_small") nil nil)) nil))
          nil))
        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)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (div_rem_small formula-decl nil div_nat nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (div_smaller formula-decl nil div_nat nil))
   nil))
(nmod_even 0
  (nmod_even-1 nil 3507028517
   ("" (skosimp*)
    (("" (expand "nmod") (("" (rewrite "div_even") nil nil)) nil)) nil)
   ((nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (nmod const-decl "below(m)" mod_nat nil)
    (nat nonempty-type-eq-decl nil naturalnumbers 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)
    (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)
    (div_even formula-decl nil div_nat nil))
   nil))
(nmod_lt_nat 0
  (nmod_lt_nat-1 nil 3507028517
   ("" (skosimp*)
    (("" (expand "nmod")
      (("" (use "div_is_0") (("" (assert) nil nil)) nil)) nil))
    nil)
   ((nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (nmod const-decl "below(m)" mod_nat nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (div_is_0 formula-decl nil div_nat nil))
   nil))
(nmod_sum 0
  (nmod_sum-1 nil 3507028517
   ("" (skosimp*)
    (("" (expand "nmod")
      (("" (use "div_sum_nat") (("" (assert) nil nil)) nil)) nil))
    nil)
   ((mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (nmod const-decl "below(m)" mod_nat nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (div_sum_nat formula-decl nil div_nat nil))
   nil))
(nmod_sum_nat 0
  (nmod_sum_nat-1 nil 3507028517
   ("" (skosimp*)
    (("" (expand "nmod")
      (("" (lift-if)
        (("" (prop)
          (("1" (lemma "div_is_0")
            (("1" (inst?) (("1" (assert) nil nil)) nil)) nil)
           ("2" (lemma "lt_plus_lt1")
            (("2" (inst?)
              (("2" (inst -1 "m!1" "m!1")
                (("2" (split -1)
                  (("1" (lemma "div_sum_nat")
                    (("1" (inst -1 "-1" "m!1" "n1!1+n2!1")
                      (("1" (assert)
                        (("1" (lemma "div_is_0")
                          (("1" (inst?) (("1" (assert) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (assert) nil nil) ("3" (propax) nil nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (nmod const-decl "below(m)" mod_nat nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers 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)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (div_is_0 formula-decl nil div_nat nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (even_times_int_is_even application-judgement "even_int" integers
     nil)
    (posint_times_posint_is_posint application-judgement "posint"
     integers nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nzint_times_nzint_is_nzint application-judgement "nzint" integers
     nil)
    (div_sum_nat formula-decl nil div_nat nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (lt_plus_lt1 formula-decl nil real_props nil))
   nil))
(nmod_it_is 0
  (nmod_it_is-1 nil 3507028517
   ("" (skosimp*)
    (("" (expand "nmod")
      (("" (replace -1)
        (("" (hide -1)
          (("" (lemma "div_sum_nat")
            (("" (inst -1 "c!1" "m!1" "k!1")
              (("" (assert)
                (("" (replace -1)
                  (("" (hide -1)
                    (("" (lemma "div_is_0")
                      (("" (inst?) (("" (assert) nil nil)) nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (nmod const-decl "below(m)" mod_nat 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)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (div_is_0 formula-decl nil div_nat 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)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (div_sum_nat formula-decl nil div_nat nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil))
   nil))
(nmod_zero 0
  (nmod_zero-1 nil 3507028517
   ("" (skosimp*) (("" (grind) nil nil)) nil)
   ((div const-decl "upto(n)" div_nat nil)
    (nmod const-decl "below(m)" mod_nat nil)
    (nnrat_div_posrat_is_nnrat application-judgement "nonneg_rat"
     rationals nil)
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil 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)
    (int_minus_int_is_int application-judgement "int" integers nil))
   nil))
(nmod_one 0
  (nmod_one-1 nil 3507028517
   ("" (skosimp*)
    (("" (expand "nmod")
      (("" (lift-if)
        (("" (prop)
          (("1" (replace -1)
            (("1" (hide -1)
              (("1" (expand "div") (("1" (assert) nil nil)) nil)) nil))
            nil)
           ("2" (rewrite "div_one") (("2" (assert) nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (nmod const-decl "below(m)" mod_nat nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (div const-decl "upto(n)" div_nat nil)
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (int_times_even_is_even application-judgement "even_int" integers
     nil)
    (odd_minus_even_is_odd application-judgement "odd_int" integers
     nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props 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)
    (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)
    (div_one formula-decl nil div_nat nil))
   nil))
(nmod_of_nmod 0
  (nmod_of_nmod-1 nil 3507028517
   ("" (skosimp*)
    (("" (rewrite "nmod")
      (("" (lemma "nmod_sum")
        (("" (inst -1 "-div(k!1,m!1)" "m!1" "n!1+k!1")
          (("" (assert)
            (("" (hide 2)
              (("" (lemma "div_smaller")
                (("" (inst?) (("" (assert) nil nil)) nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((nmod const-decl "below(m)" mod_nat 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)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil 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)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (minus_int_is_int application-judgement "int" integers nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (div const-decl "upto(n)" div_nat nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (div_smaller formula-decl nil div_nat nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nmod_sum formula-decl nil mod_nat nil))
   nil))
(nmod_mult 0
  (nmod_mult-1 nil 3507028517
   ("" (skosimp*)
    (("" (rewrite "nmod")
      (("" (lemma "nmod_sum")
        (("" (inst -1 "-div(n!1, mk!1 * m!1) * mk!1" "m!1" "n!1")
          (("" (assert)
            (("" (lemma "div_smaller")
              (("" (inst?) (("" (assert) nil nil)) nil)) nil))
            nil))
          nil))
        nil))
      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)
    (nmod const-decl "below(m)" mod_nat 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)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (div const-decl "upto(n)" div_nat nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (div_smaller formula-decl nil div_nat 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)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (minus_int_is_int application-judgement "int" integers nil)
    (nmod_sum formula-decl nil mod_nat nil))
   nil)))

¤ Dauer der Verarbeitung: 0.4 Sekunden (vorverarbeitet) ¤

Download des Quellennavigators
Download des 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.