Quelle real_order.prf Sprache: Lisp

(real_order
(real_ord_ep_well_founded 0
  (real_ord_ep_well_founded-1 nil 3595171480
   ("" (skeep)
    (("" (expand "well_founded?")
      (("" (skeep)
        (("" (skolem - "a")
          ((""
            (name "Kset"
                  "{kk:nat | EXISTS (x:(p)): kk = floor(abs(x)/epsil)}")
            (("" (name "mm" "min(Kset)")
              (("1" (typepred "mm")
                (("1" (copy -1)
                  (("1" (expand "Kset" -1)
                    (("1" (skolem - "yy")
                      (("1" (inst + "yy")
                        (("1" (skeep)
                          (("1" (inst - "floor(abs(x)/epsil)")
                            (("1" (split -)
                              (("1"
                                (expand "real_ord_ep")
                                (("1" (assert) nil nil))
                                nil)
                               ("2"
                                (expand "Kset" 1)
                                (("2" (inst + "x") nil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (hide 2)
                (("2" (expand "nonempty?")
                  (("2" (expand "empty?")
                    (("2" (expand "member")
                      (("2" (inst - "floor(abs(a)/epsil)")
                        (("2" (expand "Kset" 1)
                          (("2" (inst + "a") nil nil)) nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((well_founded? const-decl "bool" orders nil)
    (set type-eq-decl nil sets nil)
    (nonempty? const-decl "bool" sets nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (min const-decl "{a | S(a) AND (FORALL x: S(x) IMPLIES a <= x)}"
         min_nat 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)
    (real_ord_ep const-decl "bool" real_order nil)
    (Kset skolem-const-decl "[nat -> boolean]" real_order nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (member const-decl "bool" sets nil)
    (a skolem-const-decl "real" real_order nil)
    (p skolem-const-decl "pred[real]" real_order nil)
    (empty? const-decl "bool" sets nil)
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (nnreal_div_posreal_is_nnreal application-judgement "nnreal"
     real_types 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 "[T, T -> boolean]" equalities nil)
    (pred type-eq-decl nil defined_types nil)
    (integer nonempty-type-from-decl nil integers nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil)
    (/= const-decl "boolean" notequal nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil))
   nil))
(real_ord_ep_decreases_halves 0
  (real_ord_ep_decreases_halves-1 nil 3595172081
   ("" (skeep)
    (("" (case "FORALL (y:real): y>=1 IMPLIES floor(y/2) < floor(y)")
      (("1" (inst - "abs(x)/epsil")
        (("1" (assert)
          (("1" (split -1)
            (("1" (expand "real_ord_ep")
              (("1" (assert)
                (("1" (expand "abs")
                  (("1" (lift-if)
                    (("1" (lift-if)
                      (("1" (lift-if) (("1" (ground) nil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (cross-mult 1) nil nil))
            nil))
          nil))
        nil)
       ("2" (hide-all-but 1)
        (("2" (skeep) (("2" (ground) nil nil)) nil)) nil))
      nil))
    nil)
   ((/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (floor const-decl "{i | i <= x & x < i + 1}" floor_ceil nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (integer nonempty-type-from-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) (>= const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans 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)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (real_ord_ep_well_founded application-judgement
     "(well_founded?[real])" real_order nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (div_mult_pos_ge1 formula-decl nil real_props nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (real_ord_ep const-decl "bool" real_order nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nonneg_floor_is_nat application-judgement "nat" floor_ceil nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nnreal_div_posreal_is_nnreal application-judgement "nnreal"
     real_types nil))
   shostak)))

quality92%

¤ Dauer der Verarbeitung: 0.13 Sekunden (vorverarbeitet) ¤

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Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

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