Quelle min_array.prf Sprache: Lisp

(min_array
(imin_TCC1 0
  (imin_TCC1-1 nil 3281095831
   ("" (inst 1 "(LAMBDA A: Imin(A,0,N-1))")
    (("1" (skosimp*)
      (("1" (typepred "Imin(A!1, 0, N - 1)")
        (("1" (prop)
          (("1" (inst?)
            (("1" (assert) nil nil) ("2" (assert) nil nil)
             ("3" (assert) nil nil))
            nil)
           ("2" (assert) nil nil)
           ("3" (inst?)
            (("1" (assert)
              (("1" (assert)
                (("1" (skosimp*)
                  (("1" (assert)
                    (("1" (typepred "Imin(A!1, 0, N - 1)")
                      (("1" (inst?) (("1" (assert) nil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (skosimp*) (("2" (assert) nil nil)) nil)
             ("3" (assert) nil nil))
            nil))
          nil)
         ("2" (assert) nil nil) ("3" (assert) nil nil))
        nil))
      nil)
     ("2" (skosimp*) (("2" (assert) nil nil)) nil)
     ("3" (skosimp*) (("3" (assert) nil nil)) nil))
    nil)
   ((A!1 skolem-const-decl "[below(N) -> T]" min_array 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)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (Imin const-decl
     "{i: subrange(ii, jj) | (FORALL j: ii <= j AND j <= jj IMPLIES A(i) <= A(j))}"
     min_array_def nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (subrange type-eq-decl nil integers nil)
    (abv type-eq-decl nil min_array_def nil)
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= formal-const-decl "(total_order?[T])" min_array nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (T formal-type-decl nil min_array nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N formal-const-decl "posnat" min_array 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)
    (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))
   nil))
(min_TCC1 0
  (min_TCC1-1 nil 3281095831
   ("" (inst 1 "(LAMBDA A: A(imin(A)))")
    (("" (skosimp*)
      (("" (prop)
        (("1" (skosimp*)
          (("1" (typepred "imin(A!1)") (("1" (inst?) nil)))))
         ("2" (inst?) nil))))))
    nil)
   ((NOT const-decl "[bool -> bool]" booleans nil)
    (imin const-decl "{i: below(N) | (FORALL ii: A(i) <= A(ii))}"
     min_array nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (<= formal-const-decl "(total_order?[T])" min_array nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (T formal-type-decl nil min_array nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N formal-const-decl "posnat" min_array 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)
    (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))
(min_lem 0
  (min_lem-1 nil 3281095831
   ("" (skosimp*) (("" (typepred "min(A!1)") (("" (inst?) nil)))) 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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= formal-const-decl "(total_order?[T])" min_array nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (T formal-type-decl nil min_array nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N formal-const-decl "posnat" min_array 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))
   nil))
(min_in? 0
  (min_in?-1 nil 3281095831
   ("" (skosimp*)
    (("" (typepred "min(A!1)")
      (("" (skosimp*)
        (("" (expand "in?")
          (("" (hide -1) (("" (inst?) (("" (assert) nil))))))))))))
    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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= formal-const-decl "(total_order?[T])" min_array nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (T formal-type-decl nil min_array nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N formal-const-decl "posnat" min_array 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)
    (in? const-decl "bool" below_arrays nil))
   nil))
(min_def 0
  (min_def-1 nil 3281095831
   ("" (skosimp*)
    (("" (typepred "min(A!1)")
      (("" (skosimp*)
        (("" (inst?)
          (("" (assert) (("" (hide -1) (("" (grind) nil))))))))))))
    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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= formal-const-decl "(total_order?[T])" min_array nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (T formal-type-decl nil min_array nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N formal-const-decl "posnat" min_array 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)
    (in? const-decl "bool" below_arrays nil))
   nil))
(min_it_is 0
  (min_it_is-1 nil 3281095831
   ("" (skosimp*)
    (("" (expand "in?")
      (("" (skosimp*)
        (("" (replace -2)
          (("" (hide -2)
            (("" (typepred "min(A!1)")
              (("" (skosimp*)
                (("" (replace -2 * rl)
                  (("" (hide -2)
                    (("" (inst?)
                      (("" (inst?)
                        (("" (assert)
                          (("" (typepred "<=")
                            (("" (expand "total_order?")
                              ((""
                                (expand "partial_order?")
                                ((""
                                  (flatten)
                                  ((""
                                    (expand "antisymmetric?")
                                    ((""
                                      (inst?)
                                      ((""
                                        (assert)
                                        nil))))))))))))))))))))))))))))))))))))
    nil)
   ((in? const-decl "bool" below_arrays 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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= formal-const-decl "(total_order?[T])" min_array nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (T formal-type-decl nil min_array nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N formal-const-decl "posnat" min_array 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)
    (antisymmetric? const-decl "bool" relations nil)
    (partial_order? const-decl "bool" orders nil))
   nil))
(imin_lem 0
  (imin_lem-1 nil 3281095831
   ("" (skosimp*)
    (("" (typepred "imin(A!1)")
      (("" (typepred "min(A!1)")
        (("" (skosimp*)
          (("" (replace -2 * rl)
            (("" (hide -2)
              (("" (inst?)
                (("" (inst -3 "jj!1")
                  (("" (typepred "min_array.<=")
                    (("" (expand "total_order?")
                      (("" (expand "partial_order?")
                        (("" (flatten)
                          (("" (expand "antisymmetric?")
                            (("" (inst?)
                              ((""
                                (assert)
                                nil))))))))))))))))))))))))))))
    nil)
   ((imin const-decl "{i: below(N) | (FORALL ii: A(i) <= A(ii))}"
     min_array nil)
    (<= formal-const-decl "(total_order?[T])" min_array nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (T formal-type-decl nil min_array nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N formal-const-decl "posnat" min_array nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers 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)
    (< const-decl "bool" reals 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_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (antisymmetric? const-decl "bool" relations nil)
    (partial_order? const-decl "bool" orders nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (min const-decl
         "{t: T | (FORALL ii: t <= A(ii)) AND (EXISTS jj: A(jj) = t)}"
         min_array nil))
   nil))
(imin_1 0
  (imin_1-1 nil 3281095831
   ("" (skosimp*) (("" (typepred "imin(A!1)") (("" (assert) nil))))
    nil)
   ((imin const-decl "{i: below(N) | (FORALL ii: A(i) <= A(ii))}"
     min_array nil)
    (<= formal-const-decl "(total_order?[T])" min_array nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (T formal-type-decl nil min_array nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N formal-const-decl "posnat" min_array nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers 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)
    (< const-decl "bool" reals 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_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
(min_2_TCC1 0
  (min_2_TCC1-1 nil 3281095831 ("" (subtype-tcc) nil nil)
   ((real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
(min_2_TCC2 0
  (min_2_TCC2-1 nil 3281095831 ("" (subtype-tcc) nil nil)
   ((real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
(min_2 0
  (min_2-1 nil 3281095831
   ("" (skosimp*)
    (("" (typepred "min(A!1)")
      (("" (skosimp*)
        (("" (replace -2 * rl)
          (("" (case "jj!1 = 0 OR jj!1 = 1")
            (("1" (split -1)
              (("1" (replace -1)
                (("1" (hide -1)
                  (("1" (lift-if)
                    (("1" (inst -1 "1")
                      (("1" (ground) nil) ("2" (assert) nil)))))))))
               ("2" (replace -1)
                (("2" (hide -1)
                  (("2" (inst -1 "0")
                    (("2" (lift-if)
                      (("2" (ground)
                        (("2" (hide -3 -4)
                          (("2" (typepred "min_array.<=")
                            (("2" (expand "total_order?")
                              (("2"
                                (expand "partial_order?")
                                (("2"
                                  (flatten)
                                  (("2"
                                    (hide -1 -3)
                                    (("2"
                                      (expand "antisymmetric?")
                                      (("2"
                                        (inst?)
                                        (("2"
                                          (assert)
                                          nil)))))))))))))))))))))))))))))
             ("2" (hide 2 -1 -2)
              (("2" (typepred "jj!1")
                (("2" (replace -2) (("2" (ground) nil))))))))))))))))
    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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= formal-const-decl "(total_order?[T])" min_array nil)
    (total_order? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (T formal-type-decl nil min_array nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N formal-const-decl "posnat" min_array 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)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (antisymmetric? const-decl "bool" relations nil)
    (partial_order? const-decl "bool" orders nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil))
   nil)))

quality100%

¤ Dauer der Verarbeitung: 0.13 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

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.