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Datei: real_fun_props.prf Sprache: Lisp

Original von: PVS^©

(real_fun_props
(strict_incr_to_incr 0
  (strict_incr_to_incr-1 nil 3506273132
   ("" (grind :if-match nil)
    (("" (inst -3 "x!1" "y!1") (("" (assert) nil nil)) nil)) nil)
   ((real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props 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)
    (T_pred const-decl "[real -> boolean]" real_fun_props nil)
    (T formal-subtype-decl nil real_fun_props nil)
    (increasing? const-decl "bool" real_fun_preds nil)
    (strict_increasing? const-decl "bool" real_fun_preds nil))
   nil))
(strict_decr_to_decr 0
  (strict_decr_to_decr-1 nil 3506273132
   ("" (grind :if-match nil)
    (("" (inst -3 "x!1" "y!1") (("" (assert) nil nil)) nil)) nil)
   ((real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props 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)
    (T_pred const-decl "[real -> boolean]" real_fun_props nil)
    (T formal-subtype-decl nil real_fun_props nil)
    (decreasing? const-decl "bool" real_fun_preds nil)
    (strict_decreasing? const-decl "bool" real_fun_preds nil))
   nil))
(incr_neg 0
  (incr_neg-1 nil 3506273132 ("" (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)
    (T_pred const-decl "[real -> boolean]" real_fun_props nil)
    (T formal-subtype-decl nil real_fun_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (- const-decl "[T -> real]" real_fun_ops nil)
    (increasing? const-decl "bool" real_fun_preds nil)
    (decreasing? const-decl "bool" real_fun_preds nil))
   nil))
(decr_neg 0
  (decr_neg-1 nil 3506273132 ("" (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)
    (T_pred const-decl "[real -> boolean]" real_fun_props nil)
    (T formal-subtype-decl nil real_fun_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (- const-decl "[T -> real]" real_fun_ops nil)
    (decreasing? const-decl "bool" real_fun_preds nil)
    (increasing? const-decl "bool" real_fun_preds nil))
   nil))
(strict_incr_neg 0
  (strict_incr_neg-1 nil 3506273132 ("" (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)
    (T_pred const-decl "[real -> boolean]" real_fun_props nil)
    (T formal-subtype-decl nil real_fun_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (- const-decl "[T -> real]" real_fun_ops nil)
    (strict_increasing? const-decl "bool" real_fun_preds nil)
    (strict_decreasing? const-decl "bool" real_fun_preds nil))
   nil))
(strict_decr_neg 0
  (strict_decr_neg-1 nil 3506273132 ("" (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)
    (T_pred const-decl "[real -> boolean]" real_fun_props nil)
    (T formal-subtype-decl nil real_fun_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (- const-decl "[T -> real]" real_fun_ops nil)
    (strict_decreasing? const-decl "bool" real_fun_preds nil)
    (strict_increasing? const-decl "bool" real_fun_preds nil))
   nil))
(constant_to_incr 0
  (constant_to_incr-1 nil 3506273132 ("" (grind :if-match all) nil nil)
   ((f!1 skolem-const-decl "[T -> real]" real_fun_props nil)
    (x!1 skolem-const-decl "T" real_fun_props nil)
    (y!1 skolem-const-decl "T" real_fun_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (T formal-subtype-decl nil real_fun_props nil)
    (T_pred const-decl "[real -> boolean]" real_fun_props 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)
    (constant? const-decl "bool" real_fun_preds nil)
    (increasing? const-decl "bool" real_fun_preds nil))
   nil))
(constant_to_decr 0
  (constant_to_decr-1 nil 3506273132 ("" (grind :if-match all) nil nil)
   ((f!1 skolem-const-decl "[T -> real]" real_fun_props nil)
    (y!1 skolem-const-decl "T" real_fun_props nil)
    (x!1 skolem-const-decl "T" real_fun_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (T formal-subtype-decl nil real_fun_props nil)
    (T_pred const-decl "[real -> boolean]" real_fun_props 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)
    (constant? const-decl "bool" real_fun_preds nil)
    (decreasing? const-decl "bool" real_fun_preds nil))
   nil))
(constant_neg 0
  (constant_neg-1 nil 3506273132 ("" (grind :if-match all) nil nil)
   ((x!1 skolem-const-decl "T" real_fun_props nil)
    (y!1 skolem-const-decl "T" real_fun_props 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)
    (T_pred const-decl "[real -> boolean]" real_fun_props nil)
    (T formal-subtype-decl nil real_fun_props nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (f!1 skolem-const-decl "[T -> real]" real_fun_props nil)
    (x!1 skolem-const-decl "T" real_fun_props nil)
    (y!1 skolem-const-decl "T" real_fun_props nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (- const-decl "[T -> real]" real_fun_ops nil)
    (constant? const-decl "bool" real_fun_preds nil))
   nil))
(bounded_above_neg 0
  (bounded_above_neg-1 nil 3506273132
   ("" (grind :if-match nil)
    (("1" (inst + "-a!1")
      (("1" (skolem!) (("1" (inst?) (("1" (assert) nil nil)) nil))
        nil))
      nil)
     ("2" (inst + "-a!1")
      (("2" (skolem!) (("2" (inst?) (("2" (assert) nil nil)) nil))
        nil))
      nil))
    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)
    (T formal-subtype-decl nil real_fun_props nil)
    (T_pred const-decl "[real -> boolean]" real_fun_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props 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)
    (bounded_below? const-decl "bool" real_fun_preds nil)
    (bounded_above? const-decl "bool" real_fun_preds nil)
    (- const-decl "[T -> real]" real_fun_ops nil))
   nil))
(bounded_below_neg 0
  (bounded_below_neg-1 nil 3506273132
   ("" (grind :if-match nil)
    (("1" (inst + "-a!1")
      (("1" (skolem!) (("1" (inst?) (("1" (assert) nil nil)) nil))
        nil))
      nil)
     ("2" (inst + "-a!1")
      (("2" (skolem!) (("2" (inst?) (("2" (assert) nil nil)) nil))
        nil))
      nil))
    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)
    (T formal-subtype-decl nil real_fun_props nil)
    (T_pred const-decl "[real -> boolean]" real_fun_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props 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)
    (bounded_above? const-decl "bool" real_fun_preds nil)
    (bounded_below? const-decl "bool" real_fun_preds nil)
    (- const-decl "[T -> real]" real_fun_ops nil))
   nil))
(max_bounded 0
  (max_bounded-1 nil 3506273132
   ("" (grind :if-match nil) (("" (inst? +) nil 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)
    (T_pred const-decl "[real -> boolean]" real_fun_props nil)
    (T formal-subtype-decl nil real_fun_props nil)
    (bounded_above? const-decl "bool" real_fun_preds nil)
    (is_maximum? const-decl "bool" real_fun_preds nil))
   nil))
(min_bounded 0
  (min_bounded-1 nil 3506273132
   ("" (grind :if-match nil) (("" (inst? +) nil 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)
    (T_pred const-decl "[real -> boolean]" real_fun_props nil)
    (T formal-subtype-decl nil real_fun_props nil)
    (bounded_below? const-decl "bool" real_fun_preds nil)
    (is_minimum? const-decl "bool" real_fun_preds nil))
   nil))
(max_neg 0
  (max_neg-1 nil 3506273132
   ("" (grind :if-match nil)
    (("1" (inst -3 "y!1") (("1" (assert) nil nil)) nil)
     ("2" (inst?) (("2" (assert) nil nil)) nil))
    nil)
   ((minus_real_is_real application-judgement "real" reals nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props 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)
    (T_pred const-decl "[real -> boolean]" real_fun_props nil)
    (T formal-subtype-decl nil real_fun_props nil)
    (is_minimum? const-decl "bool" real_fun_preds nil)
    (is_maximum? const-decl "bool" real_fun_preds nil)
    (- const-decl "[T -> real]" real_fun_ops nil))
   nil))
(min_neg 0
  (min_neg-1 nil 3506273132
   ("" (skosimp*)
    (("" (rewrite "max_neg" :dir rl)
      (("" (case-replace "--f!1 = f!1")
        (("1" (assert) nil nil)
         ("2" (hide 2)
          (("2" (apply-extensionality 1 :hide? t)
            (("2" (grind) nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((max_neg formula-decl nil real_fun_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)
    (T_pred const-decl "[real -> boolean]" real_fun_props nil)
    (T formal-subtype-decl nil real_fun_props nil)
    (- const-decl "[T -> real]" real_fun_ops nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (= const-decl "[T, T -> boolean]" equalities nil))
   nil)))

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