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Datei: arrays_examples.pvs   Sprache: Lisp

Untersuchung PVS©

(sort_array_lems
 (sort_min_TCC1 0
  (sort_min_TCC1-1 nil 3506271670 ("" (subtype-tcc) nil nil)
   ((real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
 (sort_min 0
  (sort_min-1 nil 3506271670
   ("" (skosimp*)
    (("" (typepred "sort(A!1)")
      (("" (typepred "min(A!1)")
        (("" (skosimp*)
          (("" (expand "permutation_of?")
            (("" (skosimp*)
              (("" (expand "bijective?")
                (("" (flatten)
                  (("" (expand "surjective?")
                    (("" (inst -4 "0")
                      (("" (skosimp*)
                        (("" (inst -5 "x!1")
                          (("" (replace -4)
                            (("" (hide -4)
                              ((""
                                (inst -1 "x!1")
                                ((""
                                  (reveal -3)
                                  ((""
                                    (inst -1 "jj!1")
                                    ((""
                                      (expand "sorted?")
                                      ((""
                                        (inst -6 "0" "f!1(jj!1)")
                                        ((""
                                          (replace -1 * rl)
                                          ((""
                                            (assert)
                                            ((""
                                              (hide -1)
                                              ((""
                                                (replace -2)
                                                ((""
                                                  (replace -4)
                                                  ((""
                                                    (hide -2 -3 -4)
                                                    ((""
                                                      (typepred
                                                       "sort_array_lems.<=")
                                                      ((""
                                                        (expand
                                                         "total_order?")
                                                        ((""
                                                          (expand
                                                           "partial_order?")
                                                          ((""
                                                            (flatten)
                                                            ((""
                                                              (expand
                                                               "antisymmetric?")
                                                              ((""
                                                                (inst?)
                                                                ((""
                                                                  (assert)
                                                                  nil))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
    nil)
   ((sort const-decl "{a | permutation_of?(A, a) AND sorted?(a)}"
      sort_array nil)
    (sorted? const-decl "bool" sort_array nil)
    (<= formal-const-decl "(total_order?[T])" sort_array_lems nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (below_array type-eq-decl nil below_arrays nil)
    (permutation_of? const-decl "bool" permutations nil)
    (T formal-type-decl nil sort_array_lems nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N formal-const-decl "posnat" sort_array_lems 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)
    (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)
    (below type-eq-decl nil nat_types nil)
    (partial_order? const-decl "bool" orders nil)
    (antisymmetric? const-decl "bool" relations nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (surjective? const-decl "bool" functions nil)
    (bijective? const-decl "bool" functions nil)
    (min const-decl
         "{t: T | (FORALL ii: t <= A(ii)) AND (EXISTS jj: A(jj) = t)}"
         min_array nil)
    (= const-decl "[T, T -> boolean]" equalities nil))
   nil))
 (sort_max_TCC1 0
  (sort_max_TCC1-1 nil 3506271670 ("" (subtype-tcc) nil 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_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
 (sort_max 0
  (sort_max-1 nil 3506271670
   ("" (skosimp*)
    (("" (typepred "sort(A!1)")
      (("" (typepred "max(A!1)")
        (("" (expand "sorted?")
          (("" (skosimp*)
            (("" (expand "permutation_of?")
              (("" (skosimp*)
                (("" (inst-cp -4 "jj!1")
                  (("" (expand "bijective?")
                    (("" (flatten)
                      (("" (expand "surjective?")
                        (("" (inst -4 "N-1")
                          (("" (skosimp*)
                            (("" (inst -5 "x!1")
                              ((""
                                (replace -4)
                                ((""
                                  (hide -4)
                                  ((""
                                    (inst -1 "x!1")
                                    ((""
                                      (replace -4)
                                      ((""
                                        (hide -4)
                                        ((""
                                          (inst -5 "f!1(jj!1)" "N-1")
                                          ((""
                                            (assert)
                                            ((""
                                              (replace -2)
                                              ((""
                                                (hide -2)
                                                ((""
                                                  (replace -3 * rl)
                                                  ((""
                                                    (hide -2 -3)
                                                    ((""
                                                      (typepred
                                                       "sort_array_lems.<=")
                                                      ((""
                                                        (expand
                                                         "total_order?")
                                                        ((""
                                                          (expand
                                                           "partial_order?")
                                                          ((""
                                                            (flatten)
                                                            ((""
                                                              (expand
                                                               "antisymmetric?")
                                                              ((""
                                                                (inst?)
                                                                ((""
                                                                  (assert)
                                                                  nil))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
    nil)
   ((sort const-decl "{a | permutation_of?(A, a) AND sorted?(a)}"
      sort_array nil)
    (sorted? const-decl "bool" sort_array nil)
    (<= formal-const-decl "(total_order?[T])" sort_array_lems nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (below_array type-eq-decl nil below_arrays nil)
    (permutation_of? const-decl "bool" permutations nil)
    (T formal-type-decl nil sort_array_lems nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N formal-const-decl "posnat" sort_array_lems 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)
    (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)
    (below type-eq-decl nil nat_types nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (partial_order? const-decl "bool" orders nil)
    (antisymmetric? const-decl "bool" relations nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (surjective? const-decl "bool" functions nil)
    (bijective? const-decl "bool" functions nil)
    (max const-decl
         "{t: T | (FORALL ii: A(ii) <= t) AND (EXISTS jj: A(jj) = t)}"
         max_array nil)
    (= const-decl "[T, T -> boolean]" equalities nil))
   nil)))


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