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Datei: extended_nnreal.summary   Sprache: Unknown

Original von: PVS©

(branch_and_bound_X
 (emptyDirVars_TCC1 0
  (emptyDirVars_TCC1-1 nil 3546959448 ("" (grind) nil nil)
   ((length def-decl "nat" list_props nil)) nil))
 (length_empty 0
  (length_empty-1 nil 3546943024 ("" (grind) nil nil)
   ((emptyDirVars const-decl "DirVarStack" branch_and_bound_X nil))
   shostak))
 (topDirVar_TCC1 0
  (topDirVar_TCC1-2 nil 3546959497
   ("" (skeep :preds? t)
    (("" (typepred "stack(dirvars)") (("" (grind) nil nil)) nil)) nil)
   ((nonempty? const-decl "bool" branch_and_bound_X nil)
    (DirVarStack type-eq-decl nil branch_and_bound_X nil)
    (stack type-eq-decl nil stack nil)
    (length def-decl "nat" list_props 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)
    (list type-decl nil list_adt nil)
    (DirVar type-eq-decl nil branch_and_bound_X nil)
    (VarType formal-type-decl nil branch_and_bound_X nil)
    (= const-decl "[T, T -> boolean]" equalities 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)
    (top const-decl "Maybe[T]" stack nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil)
  (topDirVar_TCC1-1 nil 3546959448 ("" (subtype-tcc) nil nilnil nil))
 (pushDirVar_TCC1 0
  (pushDirVar_TCC1-2 nil 3546959526
   ("" (skeep)
    (("" (typepred "stack(dirvars)") (("" (grind) nil nil)) nil)) nil)
   ((DirVarStack type-eq-decl nil branch_and_bound_X nil)
    (stack type-eq-decl nil stack nil)
    (length def-decl "nat" list_props 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)
    (list type-decl nil list_adt nil)
    (DirVar type-eq-decl nil branch_and_bound_X nil)
    (VarType formal-type-decl nil branch_and_bound_X nil)
    (= const-decl "[T, T -> boolean]" equalities 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)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (push const-decl "stack" stack nil))
   nil)
  (pushDirVar_TCC1-1 nil 3546959448 ("" (subtype-tcc) nil nilnil
   nil))
 (pushDirVar_TCC2 0
  (pushDirVar_TCC2-1 nil 3546959448 ("" (grind) nil nil)
   ((real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (push const-decl "stack" stack nil)
    (nonempty? const-decl "bool" branch_and_bound_X nil))
   nil))
 (popDirVar_TCC1 0
  (popDirVar_TCC1-1 nil 3546959448 ("" (subtype-tcc) nil nil)
   ((int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   nil))
 (popDirVar_TCC2 0
  (popDirVar_TCC2-2 nil 3546959629
   ("" (skeep)
    (("" (typepred "stack(dirvars)")
      (("" (expand "length" -1) (("" (grind) nil nil)) nil)) nil))
    nil)
   ((DirVarStack type-eq-decl nil branch_and_bound_X nil)
    (stack type-eq-decl nil stack nil)
    (length def-decl "nat" list_props 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)
    (list type-decl nil list_adt nil)
    (DirVar type-eq-decl nil branch_and_bound_X nil)
    (VarType formal-type-decl nil branch_and_bound_X nil)
    (= const-decl "[T, T -> boolean]" equalities 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)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (pop const-decl "stack" stack nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil))
   nil)
  (popDirVar_TCC2-1 nil 3546959448 ("" (subtype-tcc) nil nilnil nil))
 (branch_and_bound_TCC1 0
  (branch_and_bound_TCC1-1 nil 3521295757 ("" (subtype-tcc) nil nil)
   nil nil))
 (branch_and_bound_TCC2 0
  (branch_and_bound_TCC2-1 nil 3521298539 ("" (subtype-tcc) 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)
    (>= const-decl "bool" 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (VarType formal-type-decl nil branch_and_bound_X nil)
    (DirVar type-eq-decl nil branch_and_bound_X nil)
    (list type-decl nil list_adt nil)
    (stack type-eq-decl nil stack nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (length def-decl "nat" list_props nil)
    (DirVarStack type-eq-decl nil branch_and_bound_X nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   nil))
 (branch_and_bound_TCC3 0
  (branch_and_bound_TCC3-1 nil 3521298539
   ("" (termination-tcc) 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)
    (>= const-decl "bool" 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (VarType formal-type-decl nil branch_and_bound_X nil)
    (DirVar type-eq-decl nil branch_and_bound_X nil)
    (list type-decl nil list_adt nil)
    (stack type-eq-decl nil stack nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (length def-decl "nat" list_props nil)
    (DirVarStack type-eq-decl nil branch_and_bound_X nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (push const-decl "stack" stack nil)
    (pushDirVar const-decl "(nonempty?)" branch_and_bound_X nil))
   nil))
 (branch_and_bound_TCC4 0
  (branch_and_bound_TCC4-1 nil 3546942913 ("" (subtype-tcc) nil nil)
   ((push const-decl "stack" stack nil)
    (pushDirVar const-decl "(nonempty?)" branch_and_bound_X nil)
    (int_minus_int_is_int application-judgement "int" integers nil))
   nil))
 (branch_and_bound_TCC5 0
  (branch_and_bound_TCC5-1 nil 3546942913
   ("" (termination-tcc) 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)
    (>= const-decl "bool" 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (VarType formal-type-decl nil branch_and_bound_X nil)
    (DirVar type-eq-decl nil branch_and_bound_X nil)
    (list type-decl nil list_adt nil)
    (stack type-eq-decl nil stack nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (length def-decl "nat" list_props nil)
    (DirVarStack type-eq-decl nil branch_and_bound_X nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (push const-decl "stack" stack nil)
    (pushDirVar const-decl "(nonempty?)" branch_and_bound_X nil))
   nil))
 (branch_and_bound_TCC6 0
  (branch_and_bound_TCC6-1 nil 3547374379
   ("" (termination-tcc) nil nil)
   ((push const-decl "stack" stack nil)
    (pushDirVar const-decl "(nonempty?)" branch_and_bound_X nil)
    (int_minus_int_is_int application-judgement "int" integers nil))
   nil))
 (branch_and_bound_sound 0
  (branch_and_bound_sound-8 nil 3571414984
   ("" (skeep)
    ((""
      (name-replace "PP" "(evaluate, branch, subdivide,
                                                                          denorm, combine, prune, le, ge, select,accumulate,
                                                                          maxdepth)"
       :hide? nil)
      (("" (decompose-equality -1)
        ((""
          (case " FORALL (obj, dom, acc, dirvars,(depth:nat)):
                                                                                                                                                    depth = maxdepth-length(dirvars) IMPLIES
                                                                                                                                                     LET bandb = branch_and_bound(PP)(obj, dom, acc, dirvars)
                                                                                                                                                       IN sound(dom, obj, bandb`ans)")
          (("1" (skeep)
            (("1" (inst? -)
              (("1" (inst - "maxdepth-length(dirvars)")
                (("1" (assertnil nil)) nil))
              nil))
            nil)
           ("2" (hide 2)
            (("2" (induct "depth")
              (("1" (assertnil nil)
               ("2" (skeep)
                (("2" (move-terms -1 r 2)
                  (("2" (assert)
                    (("2" (expand "branch_and_bound")
                      (("2" (expand "sound_evaluate?")
                        (("2" (inst - "dom" "obj")
                          (("2" (assertnil nil)) nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("3" (skolem 1 "depth")
                (("3" (flatten)
                  (("3" (skeep)
                    (("3"
                      (name-replace "bandb"
                       "branch_and_bound(PP)(obj, dom, acc,dirvars)"
                       :hide? nil)
                      (("3"
                        (expand "branch_and_bound" -1 :assert? none)
                        (("3"
                          (label "PP"
                                 (-4
                                  -5
                                  -6
                                  -7
                                  -8
                                  -9
                                  -10
                                  -11
                                  -12
                                  -13
                                  -14))
                          (("3" (replaces "PP" :dir rl)
                            (("3" (skoletin* -1)
                              (("3"
                                (label "HI" -6)
                                (("3"
                                  (hide "HI")
                                  (("3"
                                    (expand "sound_evaluate?")
                                    (("3"
                                      (inst - "dom" "obj")
                                      (("3"
                                        (case-replace
                                         "length(dirvars) = maxdepth OR le(thisans) OR thisout`exit OR prune(dirvars, newacc1, thisans)")
                                        (("1" (assertnil nil)
                                         ("2"
                                          (flatten)
                                          (("2"
                                            (replaces :from 1 :to 4)
                                            (("2"
                                              (skoletin
                                               -1
                                               :postfix
                                               "p")
                                              (("2"
                                                (skoletin* -1)
                                                (("2"
                                                  (hide -11)
                                                  (("2"
                                                    (case-replace
                                                     "firstout`exit")
                                                    (("1"
                                                      (replaces
                                                       -2
                                                       :dir
                                                       rl)
                                                      (("1"
                                                        (assert)
                                                        (("1"
                                                          (expand
                                                           "presound_combine?")
                                                          (("1"
                                                            (inst? -)
                                                            (("1"
                                                              (assert)
                                                              (("1"
                                                                (hide
                                                                 1)
                                                                (("1"
                                                                  (case
                                                                   "sound(dom1,sp1,branch_and_bound(PP)(sp1,dom1,newacc1,pushDirVar((dirp, vp), dirvars))`ans)")
                                                                  (("1"
                                                                    (expand
                                                                     "PP")
                                                                    (("1"
                                                                      (replaces
                                                                       -3
                                                                       :dir
                                                                       rl)
                                                                      (("1"
                                                                        (expand
                                                                         "sound_subdivide?")
                                                                        (("1"
                                                                          (expand
                                                                           "le_subdivide?")
                                                                          (("1"
                                                                            (inst
                                                                             -
                                                                             "dom1"
                                                                             "dom"
                                                                             "obj"
                                                                             "vp")
                                                                            (("1"
                                                                              (replace
                                                                               -7
                                                                               :dir
                                                                               rl)
                                                                              (("1"
                                                                                (replace
                                                                                 -12
                                                                                 :dir
                                                                                 rl)
                                                                                (("1"
                                                                                  (split
                                                                                   -)
                                                                                  (("1"
                                                                                    (expand
                                                                                     "sound_branch?")
                                                                                    (("1"
                                                                                      (inst
                                                                                       -
                                                                                       "dom1"
                                                                                       "obj"
                                                                                       "nobj"
                                                                                       "vp")
                                                                                      (("1"
                                                                                        (assert)
                                                                                        (("1"
                                                                                          (flatten)
                                                                                          (("1"
                                                                                            (expand
                                                                                             "sound_dir")
                                                                                            (("1"
                                                                                              (split
                                                                                               1)
                                                                                              (("1"
                                                                                                (flatten)
                                                                                                (("1"
                                                                                                  (assert)
                                                                                                  (("1"
                                                                                                    (replace
                                                                                                     -6
                                                                                                     :dir
                                                                                                     rl)
                                                                                                    (("1"
                                                                                                      (replaces
                                                                                                       (-8
                                                                                                        -10)
                                                                                                       :hide?
                                                                                                       nil)
                                                                                                      (("1"
                                                                                                        (hide
                                                                                                         -19)
                                                                                                        (("1"
                                                                                                          (expand
                                                                                                           "presound_evaluate?")
                                                                                                          (("1"
                                                                                                            (inst
                                                                                                             -16
                                                                                                             "dom1"
                                                                                                             "branch(vp,nobj)`1"
                                                                                                             "branch(vp,obj)`1"
                                                                                                             "firstout`ans")
                                                                                                            (("1"
                                                                                                              (assert)
                                                                                                              nil
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil)
                                                                                               ("2"
                                                                                                (flatten)
                                                                                                (("2"
                                                                                                  (assert)
                                                                                                  (("2"
                                                                                                    (replace
                                                                                                     -5
                                                                                                     :dir
                                                                                                     rl)
                                                                                                    (("2"
                                                                                                      (replaces
                                                                                                       (-7
                                                                                                        -9)
                                                                                                       :hide?
                                                                                                       nil)
                                                                                                      (("2"
                                                                                                        (hide
                                                                                                         -17)
                                                                                                        (("2"
                                                                                                          (expand
                                                                                                           "presound_evaluate?")
                                                                                                          (("2"
                                                                                                            (inst
                                                                                                             -15
                                                                                                             "dom1"
                                                                                                             "branch(vp,nobj)`2"
                                                                                                             "branch(vp,obj)`2"
                                                                                                             "firstout`ans")
                                                                                                            (("2"
                                                                                                              (assert)
                                                                                                              nil
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
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--> --------------------

--> maximum size reached

--> --------------------

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