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products/Sources/formale Sprachen/PVS/exact_real_arith/

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^© Kompilation durch diese Firma

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Datei: neg.prf Sprache: Lisp

Original von: PVS^©

(neg
(cauchy_neg_TCC1 0
  (cauchy_neg_TCC1-1 nil 3507981237
   ("" (skosimp*)
    (("" (expand "cauchy_real?")
      (("" (typepred "cx!1")
        (("" (expand "cauchy_real?")
          (("" (skolem!)
            (("" (inst 1 "-x!1")
              (("" (assert)
                (("" (expand "cauchy_prop")
                  (("" (skolem!)
                    (("" (inst - "p!1")
                      (("" (assert) (("" (grind) nil nil)) nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((cauchy_real? const-decl "bool" cauchy nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (posint_exp application-judgement "posint" exponentiation nil)
    (cauchy_prop const-decl "bool" cauchy nil)
    (posnat_expt application-judgement "posnat" exponentiation nil)
    (posrat_div_posrat_is_posrat application-judgement "posrat"
     rationals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (^ const-decl "real" exponentiation 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)
    (real_times_real_is_real application-judgement "real" reals nil)
    (minus_int_is_int application-judgement "int" integers 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)
    (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)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (cauchy_real nonempty-type-eq-decl nil cauchy nil))
   nil))
(neg_lemma 0
  (neg_lemma-1 nil 3507981237
   ("" (skosimp*)
    (("" (expand "cauchy_prop")
      (("" (expand "cauchy_neg")
        (("" (split)
          (("1" (skosimp*)
            (("1" (inst - "p!1") (("1" (grind) nil nil)) nil)) nil)
           ("2" (skosimp*)
            (("2" (inst - "p!1") (("2" (grind) nil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((posint_exp application-judgement "posint" exponentiation nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (cauchy_prop const-decl "bool" cauchy 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)
    (^ const-decl "real" exponentiation nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posrat_div_posrat_is_posrat application-judgement "posrat"
     rationals nil)
    (posnat_expt application-judgement "posnat" exponentiation nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (cauchy_neg const-decl "cauchy_real" neg nil)
    (minus_int_is_int application-judgement "int" integers nil))
   nil))
(neg_cauchy_nzreal_is_cauchy_nzreal 0
  (neg_cauchy_nzreal_is_cauchy_nzreal-1 nil 3507981237
   ("" (skosimp*)
    (("" (typepred "nzcx!1")
      (("" (expand "cauchy_nzreal?")
        (("" (skolem!)
          (("" (typepred "x!1")
            (("" (inst + "-x!1")
              (("" (lemma "neg_lemma" ("x" "x!1" "cx" "nzcx!1"))
                (("" (assert) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((cauchy_nzreal nonempty-type-eq-decl nil cauchy nil)
    (cauchy_nzreal? const-decl "bool" cauchy 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)
    (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)
    (minus_nzreal_is_nzreal application-judgement "nzreal" real_types
     nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (cauchy_real nonempty-type-eq-decl nil cauchy nil)
    (cauchy_real? const-decl "bool" cauchy nil)
    (neg_lemma formula-decl nil neg nil)
    (nzreal nonempty-type-eq-decl nil reals nil)
    (/= const-decl "boolean" notequal nil))
   nil))
(neg_cauchy_posreal_is_cauchy_negreal 0
  (neg_cauchy_posreal_is_cauchy_negreal-1 nil 3507981237
   ("" (skolem!)
    (("" (typepred "pcx!1")
      (("" (expand "cauchy_negreal?")
        (("" (expand "cauchy_posreal?")
          (("" (skolem!)
            (("" (typepred "x!1")
              (("" (inst + "-x!1")
                (("" (lemma "neg_lemma" ("x" "x!1" "cx" "pcx!1"))
                  (("" (assert) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((cauchy_posreal nonempty-type-eq-decl nil cauchy nil)
    (cauchy_posreal? const-decl "bool" cauchy 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)
    (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)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (neg_lemma formula-decl nil neg nil)
    (cauchy_real? const-decl "bool" cauchy nil)
    (cauchy_real nonempty-type-eq-decl nil cauchy 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)
    (neg_cauchy_nzreal_is_cauchy_nzreal application-judgement
     "cauchy_nzreal" neg nil)
    (<= const-decl "bool" reals nil)
    (nonpos_real nonempty-type-eq-decl nil real_types nil)
    (< const-decl "bool" reals nil)
    (negreal nonempty-type-eq-decl nil real_types nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (minus_nzreal_is_nzreal application-judgement "nzreal" real_types
     nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (cauchy_negreal? const-decl "bool" cauchy nil))
   nil))
(neg_cauchy_negreal_is_cauchy_posreal 0
  (neg_cauchy_negreal_is_cauchy_posreal-1 nil 3507981237
   ("" (skolem!)
    (("" (typepred "ncx!1")
      (("" (expand "cauchy_negreal?")
        (("" (skolem!)
          (("" (expand "cauchy_posreal?")
            (("" (inst + "-x!1")
              (("" (typepred "x!1")
                (("" (lemma "neg_lemma" ("x" "x!1" "cx" "ncx!1"))
                  (("" (assert) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((cauchy_negreal nonempty-type-eq-decl nil cauchy nil)
    (cauchy_negreal? const-decl "bool" cauchy 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)
    (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)
    (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)
    (minus_nzreal_is_nzreal application-judgement "nzreal" real_types
     nil)
    (negreal nonempty-type-eq-decl nil real_types nil)
    (< const-decl "bool" reals nil)
    (nonpos_real nonempty-type-eq-decl nil real_types nil)
    (<= const-decl "bool" reals nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields 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)
    (neg_lemma formula-decl nil neg nil)
    (cauchy_real? const-decl "bool" cauchy nil)
    (cauchy_real nonempty-type-eq-decl nil cauchy nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (neg_cauchy_nzreal_is_cauchy_nzreal application-judgement
     "cauchy_nzreal" neg nil)
    (cauchy_posreal? const-decl "bool" cauchy nil))
   nil)))

¤ Dauer der Verarbeitung: 0.19 Sekunden (vorverarbeitet) ¤

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