Quellcode-Bibliothek

^© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: sum_hack.prf Sprache: Lisp

Original von: PVS^©

(sum_hack
(Sum_TCC1 0
  (Sum_TCC1-1 nil 3321196682 ("" (tcc :defs !) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (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))
(Sum_TCC2 0
  (Sum_TCC2-1 nil 3321196682 ("" (tcc :defs !) nil nil) nil nil))
(Sum_nonneg 0
  (Sum_nonneg-1 nil 3321196682
   ("" (induct-and-rewrite "j" 1 "Sum") nil 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)
    (pred type-eq-decl nil defined_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (Sum def-decl "real" sum_hack nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil))
   nil))
(Sum_zero 0
  (Sum_zero-1 nil 3321196682
   ("" (induct "j")
    (("1" (expand "Sum")
      (("1" (assert) (("1" (skosimp*) nil nil)) nil)) nil)
     ("2" (skosimp*)
      (("2" (rewrite "Sum")
        (("2" (inst?)
          (("2" (prop)
            (("1" (skosimp*)
              (("1" (inst?) (("1" (assert) nil nil)) nil)) nil)
             ("2" (inst?) (("2" (assert) nil nil)) nil)
             ("3" (typepred "F1!1(j!1)")
              (("3" (lemma "Sum_nonneg")
                (("3" (inst?) (("3" (assert) nil nil)) nil)) nil))
              nil)
             ("4" (skosimp*) (("4" (inst?) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((NOT const-decl "[bool -> bool]" booleans nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (Sum_nonneg formula-decl nil sum_hack nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (i!1 skolem-const-decl "below(1 + j!1)" sum_hack nil)
    (j!1 skolem-const-decl "nat" sum_hack nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil) (Sum def-decl "real" sum_hack nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (IFF const-decl "[bool, bool -> bool]" booleans nil)
    (nonneg_real nonempty-type-eq-decl nil real_types 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))
(Sum_pos 0
  (Sum_pos-1 nil 3321196682
   ("" (induct "j")
    (("1" (expand "Sum")
      (("1" (skosimp*) (("1" (ground) (("1" (skosimp*) nil)))))))
     ("2" (skosimp*)
      (("2" (rewrite "Sum")
        (("2" (inst?)
          (("2" (lemma "Sum_nonneg")
            (("2" (inst?)
              (("2" (prop)
                (("1" (skosimp*) (("1" (inst?) nil)))
                 ("2" (assert) nil)
                 ("3" (inst + "j!1") (("3" (assert) nil)))
                 ("4" (skosimp*)
                  (("4" (inst?) (("4" (assert) nil))))))))))))))))))
    nil)
   ((real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (i!1 skolem-const-decl "below(1 + j!1)" sum_hack nil)
    (j!1 skolem-const-decl "nat" sum_hack nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (Sum_nonneg formula-decl nil sum_hack nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil) (Sum def-decl "real" sum_hack nil)
    (> const-decl "bool" reals nil)
    (IFF const-decl "[bool, bool -> bool]" booleans nil)
    (nonneg_real nonempty-type-eq-decl nil real_types 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))
(Sum_le 0
  (Sum_le-1 nil 3321196682
   ("" (induct "j")
    (("1" (expand "Sum") (("1" (propax) nil)))
     ("2" (skosimp*)
      (("2" (expand "Sum" +)
        (("2" (inst - "F1!1 " "F2!1")
          (("2" (prop)
            (("1" (inst?) (("1" (assert) nil)))
             ("2" (skosimp*) (("2" (inst?) nil))))))))))))
    nil)
   ((int_minus_int_is_int application-judgement "int" integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (+ const-decl "[numfield, 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)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (Sum def-decl "real" sum_hack nil) (<= const-decl "bool" reals nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (nonneg_real nonempty-type-eq-decl nil real_types 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))
(Sum_ge1 0
  (Sum_ge1-1 nil 3321196682
   ("" (induct "j")
    (("1" (skosimp*) nil)
     ("2" (skosimp*)
      (("2" (rewrite "Sum")
        (("2" (inst?)
          (("2" (assert)
            (("2" (lemma "Sum_nonneg")
              (("2" (inst?)
                (("2" (inst?) (("2" (assert) nil))))))))))))))))
    nil)
   ((Sum_nonneg formula-decl nil sum_hack nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (j!1 skolem-const-decl "nat" sum_hack nil)
    (i!1 skolem-const-decl "below(1 + j!1)" sum_hack nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (Sum def-decl "real" sum_hack nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (nonneg_real nonempty-type-eq-decl nil real_types 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))
(Sum_ge 0
  (Sum_ge-1 nil 3321196682
   ("" (induct "j")
    (("1" (skosimp*) nil)
     ("2" (skosimp*)
      (("2" (rewrite "Sum")
        (("2" (inst - "F1!1" "pz!1")
          (("2" (prop)
            (("1" (assert) nil)
             ("2" (inst?)
              (("2" (assert)
                (("2" (ground)
                  (("2" (lemma "Sum_nonneg")
                    (("2" (inst?)
                      (("2" (assert) nil))))))))))))))))))))
    nil)
   ((real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (j!1 skolem-const-decl "nat" sum_hack nil)
    (i!1 skolem-const-decl "below(1 + j!1)" sum_hack nil)
    (Sum_nonneg formula-decl nil sum_hack nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (Sum def-decl "real" sum_hack nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans 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)
    (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))
(Sum_split_TCC1 0
  (Sum_split_TCC1-1 nil 3321196682 ("" (tcc) nil nil) nil nil))
(Sum_split 0
  (Sum_split-1 nil 3321196682
   ("" (induct "j")
    (("1" (skosimp*)
      (("1" (expand "Sum") (("1" (propax) nil nil)) nil)) nil)
     ("2" (skosimp*)
      (("2" (typepred "i!1")
        (("2" (expand "Sum" + (1 3))
          (("2" (lift-if)
            (("2" (ground)
              (("1" (case-replace "i!1=j!1+1")
                (("1" (expand "Sum" + 2) (("1" (propax) nil nil)) nil)
                 ("2" (assert) nil nil))
                nil)
               ("2" (inst - "F!1" "i!1") (("2" (assert) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((int_plus_int_is_int application-judgement "int" integers nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (Sum def-decl "real" sum_hack nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (upto nonempty-type-eq-decl nil naturalnumbers 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)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil))
   nil)))

¤ Dauer der Verarbeitung: 0.204 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.