Quellcode-Bibliothek

^© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: product_upto.pvs Sprache: Lisp

Original von: PVS^©

(mixed_sigmas
(IMP_sigma_TCC1 0
  (IMP_sigma_TCC1-1 nil 3537537618
   ("" (lemma "connected_domain1") (("" (propax) nil nil)) nil)
   ((connected_domain1 formula-decl nil mixed_sigmas nil)) nil))
(IMP_sigma_TCC2 0
  (IMP_sigma_TCC2-1 nil 3537537618
   ("" (lemma "connected_domain2") (("" (propax) nil nil)) nil)
   ((connected_domain2 formula-decl nil mixed_sigmas nil)) nil))
(mixed_sigmas_const_eq_TCC1 0
  (mixed_sigmas_const_eq_TCC1-1 nil 3537536439
   ("" (skeep)
    (("" (lemma "T_pred_lem[T]")
      (("" (inst - thigh tlow _)
        (("" (skeep) (("" (inst?) (("" (assert) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((T formal-subtype-decl nil mixed_sigmas nil)
    (T_pred const-decl "[int -> boolean]" mixed_sigmas 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)
    (T_pred_lem formula-decl nil sigma nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (T_low type-eq-decl nil sigma nil)
    (T_high type-eq-decl nil sigma nil)
    (<= const-decl "bool" reals nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil))
   nil))
(mixed_sigmas_const_eq_TCC2 0
  (mixed_sigmas_const_eq_TCC2-1 nil 3537536439
   ("" (skeep)
    (("" (skeep)
      (("" (lemma "T_pred_lem[H]")
        (("" (inst - "hhigh" "hlow" _)
          (("" (inst?) (("" (assert) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((bool nonempty-type-eq-decl nil booleans nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (T_high type-eq-decl nil sigma nil)
    (T_low type-eq-decl nil sigma nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (T_pred_lem formula-decl nil sigma 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)
    (H_pred const-decl "[int -> boolean]" mixed_sigmas nil)
    (H formal-subtype-decl nil mixed_sigmas nil))
   nil))
(mixed_sigmas_const_eq 0
  (mixed_sigmas_const_eq-1 nil 3537536793
   (""
    (case "FORALL (F: [T -> real], G: [H -> real], hhigh: T_high[H],
                     hlow: T_low[H], thigh: T_high[T], tlow: T_low[T]):
               (thigh - tlow = hhigh - hlow AND
                 (FORALL (i: nat):
                    i <= thigh - tlow IMPLIES F(tlow + i) = G(hlow + i)))
                IMPLIES (FORALL (i: nat):
                    i <= thigh - tlow IMPLIES sigma[T](tlow, tlow+i, F) = sigma[H](hlow, hlow+i, G))")
    (("1" (skeep)
      (("1" (inst - "F" "G" "hhigh" "hlow" "thigh" "tlow")
        (("1" (assert)
          (("1" (replace -3)
            (("1" (inst - "thigh-tlow")
              (("1" (assert) nil nil)
               ("2" (assert)
                (("2" (expand "sigma" +) (("2" (propax) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("2" (hide 2)
      (("2" (skeep)
        (("2" (induct "i")
          (("1" (assert)
            (("1" (flatten)
              (("1" (expand "sigma" +)
                (("1" (expand "sigma" +)
                  (("1" (inst - "0") (("1" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil)
           ("2" (skeep)
            (("2" (assert)
              (("2" (expand "sigma" +)
                (("2" (inst - "1+j") (("2" (assert) nil nil)) nil))
                nil))
              nil))
            nil)
           ("3" (skeep)
            (("3" (lemma "T_pred_lem[H]")
              (("3" (inst - "hhigh" "hlow" "i+hlow")
                (("3" (assert) nil nil)) nil))
              nil))
            nil)
           ("4" (skeep)
            (("4" (lemma "T_pred_lem[T]")
              (("4" (inst - "thigh" "tlow" "i+tlow")
                (("4" (assert) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("3" (hide 2)
      (("3" (skeep)
        (("3" (skeep)
          (("3" (lemma "T_pred_lem[H]")
            (("3" (inst - "hhigh" "hlow" "hlow + i1")
              (("3" (assert) nil nil)) nil))
            nil))
          nil))
        nil))
      nil)
     ("4" (hide 2)
      (("4" (skeep)
        (("4" (skeep)
          (("4" (lemma "T_pred_lem[T]")
            (("4" (inst - "thigh" "tlow" "i1+tlow")
              (("4" (assert) nil nil)) nil))
            nil))
          nil))
        nil))
      nil)
     ("5" (hide 2)
      (("5" (skeep)
        (("5" (skeep)
          (("5" (lemma "T_pred_lem[H]")
            (("5" (inst - "hhigh" "hlow" "hlow + i")
              (("5" (assert) nil nil)) nil))
            nil))
          nil))
        nil))
      nil)
     ("6" (hide 2)
      (("6" (skeep)
        (("6" (skeep)
          (("6" (lemma "T_pred_lem[T]")
            (("6" (inst - "thigh" "tlow" "i+tlow")
              (("6" (assert) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((thigh skolem-const-decl "T_high[T]" mixed_sigmas nil)
    (tlow skolem-const-decl "T_low[T]" mixed_sigmas nil)
    (hlow skolem-const-decl "T_low[H]" mixed_sigmas nil)
    (pred type-eq-decl nil defined_types nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (T_pred_lem formula-decl nil sigma nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (thigh skolem-const-decl "T_high[T]" mixed_sigmas nil)
    (tlow skolem-const-decl "T_low[T]" mixed_sigmas nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (int_plus_int_is_int application-judgement "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)
    (T_pred const-decl "[int -> boolean]" mixed_sigmas nil)
    (T formal-subtype-decl nil mixed_sigmas nil)
    (H_pred const-decl "[int -> boolean]" mixed_sigmas nil)
    (H formal-subtype-decl nil mixed_sigmas nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (T_high type-eq-decl nil sigma nil)
    (T_low type-eq-decl nil sigma nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (sigma def-decl "real" sigma nil))
   shostak))
(mixed_sigmas_eq 0
  (mixed_sigmas_eq-1 nil 3537537619
   ("" (lemma "mixed_sigmas_const_eq")
    (("" (inst - _ _ _ _ _ _ 1)
      (("" (assert)
        (("" (case "FORALL (aa:real): 1*aa = aa")
          (("1" (rewrite -1) (("1" (rewrite -1) nil nil)) nil)
           ("2" (hide-all-but 1) (("2" (assert) nil nil)) nil))
          nil))
        nil))
      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)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (mixed_sigmas_const_eq formula-decl nil mixed_sigmas nil))
   shostak)))

¤ Dauer der Verarbeitung: 0.18 Sekunden (vorverarbeitet) ¤

Download des Quellennavigators
Download des sprechenden Kalenders
Eigene Datei ansehen

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.