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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: trackAngles_2D.prf   Sprache: Lisp

Original von: PVS©

(unif_cont_fun
 (getem_scaf4 0
  (getem_scaf4-1 nil 3324907658
   ("" (skosimp*)
    ((""
      (inst 1
       "(LAMBDA (j: posnat): choose({xy: [real,real] | P3!1(xy`1,xy`2,j)})`1)"
       "(LAMBDA (j: posnat): choose({xy: [real,real] | P3!1(xy`1,xy`2,j)})`2)")
      (("1" (skosimp*)
        (("1" (inst -1 "k!1") (("1" (assertnil nil)) nil)) nil)
       ("2" (skosimp*)
        (("2" (expand "nonempty?")
          (("2" (expand "empty?")
            (("2" (expand "member")
              (("2" (inst -2 "j!1")
                (("2" (skosimp*) (("2" (inst -1 "(x!1,y!1)"nil nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((P3!1 skolem-const-decl "[[real, real, posnat] -> bool]"
     unif_cont_fun nil)
    (nonempty? const-decl "bool" sets nil)
    (set type-eq-decl nil sets 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)
    (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)
    (choose const-decl "(p)" sets nil)
    (member const-decl "bool" sets nil)
    (empty? const-decl "bool" sets nil))
   nil))
 (unif_cont_interval 0
  (unif_cont_interval-5 "FIX" 3447507474
   ("" (skosimp*)
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      (("" (flatten)
        (("" (expand "uniformly_continuous?")
          (("" (skosimp*)
            ((""
              (case "EXISTS (N: posnat): FORALL (x, y: ({xx: T | a!1 <= xx AND xx <= b!1})):
                        abs(x - y) < 1/N IMPLIES abs(f!1(x) - f!1(y)) < epsi!1")
              (("1" (skosimp*) (("1" (inst + "1/N!1"nil nil)) nil)
               ("2" (hide 2)
                (("2"
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                          EXISTS (x, y: ({xx: T | a!1 <= xx AND xx <= b!1})):
                            abs(x - y) < 1 / N AND abs(f!1(x) - f!1(y)) >= eps")
                  (("1" (skosimp*)
                    (("1" (hide 1)
                      (("1" (lemma "getem_scaf4")
                        (("1"
                          (inst -1
                           "(LAMBDA (x,y: real,n:posnat): abs(x - y) < 1 / n AND a!1 <= x AND x <= b!1 AND a!1 <= y AND y <= b!1 AND abs(f!1(x) - f!1(y)) >= eps!1)")
                          (("1" (split -1)
                            (("1" (hide -2)
                              (("1"
                                (skosimp*)
                                (("1"
                                  (name
                                   "A"
                                   "(LAMBDA (kk: posnat): {xx: real | EXISTS (j: posnat): j >= kk AND xx = XX!1(j)})")
                                  (("1"
                                    (name
                                     "alpha"
                                     "(LAMBDA (kk: posnat): lub(A(kk)))")
                                    (("1"
                                      (name
                                       "CC"
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                                      (("1"
                                        (case
                                         "a!1 <= CC AND CC <= b!1")
                                        (("1"
                                          (flatten)
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                                            (rewrite
                                             "continuous_on_def")
                                            (("1"
                                              (inst -8 "CC")
                                              (("1"
                                                (expand "convergence")
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                                                  (flatten)
                                                  (("1"
                                                    (inst -9 "eps!1/2")
                                                    (("1"
                                                      (skosimp*)
                                                      (("1"
                                                        (expand
                                                         "extend")
                                                        (("1"
                                                          (case
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                                                          (("1"
                                                            (skosimp*)
                                                            (("1"
                                                              (case
                                                               "EXISTS (nn: posnat): alpha(kk!1) - delta!1/2 < XX!1(nn) AND XX!1(nn) <= alpha(kk!1) AND nn >= kk!1")
                                                              (("1"
                                                                (skosimp*)
                                                                (("1"
                                                                  (inst
                                                                   -12
                                                                   "nn!1")
                                                                  (("1"
                                                                    (flatten)
                                                                    (("1"
                                                                      (case
                                                                       "1/nn!1 < delta!1/2")
                                                                      (("1"
                                                                        (case
                                                                         "CC - delta!1/2 <= XX!1(nn!1) AND XX!1(nn!1) <= CC + delta!1/2")
                                                                        (("1"
                                                                          (case
                                                                           "CC - delta!1 < YY!1(nn!1) AND YY!1(nn!1) < CC + delta!1")
                                                                          (("1"
                                                                            (flatten)
                                                                            (("1"
                                                                              (lemma
                                                                               "triangle")
                                                                              (("1"
                                                                                (inst
                                                                                 -1
                                                                                 "f!1(XX!1(nn!1)) -f!1(CC)"
                                                                                 "f!1(CC) - f!1(YY!1(nn!1))")
                                                                                (("1"
                                                                                  (assert)
                                                                                  (("1"
                                                                                    (inst-cp
                                                                                     -26
                                                                                     "XX!1(nn!1)")
                                                                                    (("1"
                                                                                      (inst
                                                                                       -26
                                                                                       "YY!1(nn!1)")
                                                                                      (("1"
                                                                                        (split
                                                                                         -26)
                                                                                        (("1"
                                                                                          (split
                                                                                           -27)
                                                                                          (("1"
                                                                                            (hide
                                                                                             -4
                                                                                             -5
                                                                                             -7
                                                                                             -8
                                                                                             -9
                                                                                             -11)
                                                                                            (("1"
                                                                                              (case-replace
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                                                                                              (("1"
                                                                                                (assert)
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                                                                                                nil)
                                                                                               ("2"
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                                                                                                 1)
                                                                                                (("2"
                                                                                                  (grind)
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                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil)
                                                                                           ("2"
                                                                                            (propax)
                                                                                            nil
                                                                                            nil)
                                                                                           ("3"
                                                                                            (propax)
                                                                                            nil
                                                                                            nil)
                                                                                           ("4"
                                                                                            (hide-all-but
                                                                                             (-5
                                                                                              -6
                                                                                              1))
                                                                                            (("4"
                                                                                              (name-replace
                                                                                               "xxnn"
                                                                                               "XX!1(nn!1)")
                                                                                              (("4"
                                                                                                (grind)
                                                                                                nil
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil)
                                                                                         ("2"
                                                                                          (propax)
                                                                                          nil
                                                                                          nil)
                                                                                         ("3"
                                                                                          (propax)
                                                                                          nil
                                                                                          nil)
                                                                                         ("4"
                                                                                          (hide-all-but
                                                                                           (-2
                                                                                            -3
                                                                                            1))
                                                                                          (("4"
                                                                                            (name-replace
                                                                                             "yynn"
                                                                                             "YY!1(nn!1)")
                                                                                            (("4"
                                                                                              (grind)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil)
                                                                                 ("2"
                                                                                  (lemma
                                                                                   "connected_domain")
                                                                                  (("2"
                                                                                    (expand
                                                                                     "connected?")
                                                                                    (("2"
                                                                                      (inst
                                                                                       -
                                                                                       "a!1"
                                                                                       "b!1"
                                                                                       "CC")
                                                                                      (("2"
                                                                                        (assert)
                                                                                        nil
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (hide-all-but
                                                                             (-1
                                                                              -2
                                                                              -14
                                                                              1))
                                                                            (("2"
                                                                              (flatten)
                                                                              (("2"
                                                                                (grind)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil)
                                                                         ("2"
                                                                          (assert)
                                                                          (("2"
                                                                            (hide-all-but
                                                                             (-1
                                                                              -2
                                                                              -3
                                                                              -5
                                                                              -6
                                                                              -7
                                                                              -8
                                                                              -9
                                                                              1))
                                                                            (("2"
                                                                              (name-replace
                                                                               "xxnn"
                                                                               "XX!1(nn!1)")
                                                                              (("2"
                                                                                (assert)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (assert)
                                                                        (("2"
                                                                          (assert)
                                                                          (("2"
                                                                            (hide-all-but
                                                                             (-3
                                                                              -6
                                                                              1))
                                                                            (("2"
                                                                              (case
                                                                               "1/nn!1 <= 1/kk!1")
                                                                              (("1"
                                                                                (assert)
                                                                                nil
                                                                                nil)
                                                                               ("2"
                                                                                (hide
                                                                                 -2
                                                                                 2)
                                                                                (("2"
                                                                                  (cross-mult
                                                                                   1)
                                                                                  nil
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (hide
                                                                 -9
                                                                 -11
                                                                 -12)
                                                                (("2"
                                                                  (typepred
                                                                   "lub(A(kk!1))")
                                                                  (("1"
                                                                    (expand
                                                                     "least_upper_bound?")
                                                                    (("1"
                                                                      (flatten)
                                                                      (("1"
                                                                        (inst
                                                                         -2
                                                                         "alpha(kk!1)- delta!1 / 2")
                                                                        (("1"
                                                                          (split
                                                                           -2)
                                                                          (("1"
                                                                            (assert)
                                                                            (("1"
                                                                              (replace
                                                                               -9
                                                                               -1
                                                                               rl)
                                                                              (("1"
                                                                                (assert)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (expand
                                                                             "upper_bound?")
                                                                            (("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (typepred
                                                                                 "s!1")
                                                                                (("2"
                                                                                  (replace
                                                                                   -10
                                                                                   -1
                                                                                   rl)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    (("2"
                                                                                      (skosimp*)
                                                                                      (("2"
                                                                                        (inst
                                                                                         +
                                                                                         "j!1")
                                                                                        (("2"
                                                                                          (assert)
                                                                                          (("2"
                                                                                            (replace
                                                                                             -2)
                                                                                            (("2"
                                                                                              (hide
                                                                                               -2)
                                                                                              (("2"
                                                                                                (case
                                                                                                 "CC <= XX!1(j!1)")
                                                                                                (("1"
                                                                                                  (assert)
                                                                                                  (("1"
                                                                                                    (replace
                                                                                                     -10
                                                                                                     *
                                                                                                     rl)
                                                                                                    (("1"
                                                                                                      (assert)
                                                                                                      (("1"
                                                                                                        (inst
                                                                                                         -
                                                                                                         "XX!1(j!1)")
                                                                                                        nil
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil)
                                                                                                 ("2"
                                                                                                  (inst
                                                                                                   -
                                                                                                   "XX!1(j!1)")
                                                                                                  (("2"
                                                                                                    (assert)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (hide
                                                                     2)
                                                                    (("2"
                                                                      (prop)
                                                                      (("1"
                                                                        (expand
                                                                         "nonempty?")
                                                                        (("1"
                                                                          (expand
                                                                           "empty?")
                                                                          (("1"
                                                                            (expand
                                                                             "member")
                                                                            (("1"
                                                                              (replace
                                                                               -9
                                                                               -1
                                                                               rl)
                                                                              (("1"
                                                                                (assert)
                                                                                (("1"
                                                                                  (inst
                                                                                   -1
                                                                                   "XX!1(kk!1)")
                                                                                  (("1"
                                                                                    (inst
                                                                                     +
                                                                                     "kk!1")
                                                                                    (("1"
                                                                                      (assert)
                                                                                      nil
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (expand
                                                                         "bounded_above?")
                                                                        (("2"
                                                                          (inst
                                                                           +
                                                                           "b!1")
                                                                          (("2"
                                                                            (expand
                                                                             "upper_bound?")
                                                                            (("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (typepred
                                                                                 "s!1")
                                                                                (("2"
                                                                                  (replace
                                                                                   -9
                                                                                   -1
                                                                                   rl)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    (("2"
                                                                                      (skosimp*)
                                                                                      (("2"
                                                                                        (reveal
                                                                                         -1)
                                                                                        (("2"
                                                                                          (inst
                                                                                           -1
                                                                                           "j!1")
                                                                                          (("2"
                                                                                            (assert)
                                                                                            nil
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil)
                                                           ("2"
                                                            (typepred
                                                             "glb({alphs: real | EXISTS (jj: posnat): alphs = alpha(jj)})")
                                                            (("2"
                                                              (expand
                                                               "greatest_lower_bound?")
                                                              (("2"
                                                                (flatten)
                                                                (("2"
                                                                  (expand
                                                                   "lower_bound?")
                                                                  (("2"
                                                                    (replace
                                                                     -5
                                                                     -)
                                                                    (("2"
                                                                      (inst
                                                                       -2
                                                                       "CC+delta!1/2")
                                                                      (("2"
                                                                        (assert)
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                                                                          (skosimp*)
                                                                          (("2"
                                                                            (typepred
                                                                             "s!1")
                                                                            (("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (case
                                                                                 "FORALL (ii: posnat): ii >= jj!1 IMPLIES alpha(ii) <= alpha(jj!1)")
                                                                                (("1"
                                                                                  (case
                                                                                   "(EXISTS (jk: posnat): jk >= jj!1 AND 1/jk < delta!1/2)")
                                                                                  (("1"
                                                                                    (skosimp*)
                                                                                    (("1"
                                                                                      (inst
                                                                                       2
                                                                                       "jk!1")
                                                                                      (("1"
                                                                                        (assert)
                                                                                        (("1"
                                                                                          (inst
                                                                                           -3
                                                                                           "jk!1")
                                                                                          (("1"
                                                                                            (assert)
                                                                                            (("1"
                                                                                              (inst
                                                                                               -5
                                                                                               "alpha(jk!1)")
                                                                                              (("1"
                                                                                                (assert)
                                                                                                (("1"
                                                                                                  (inst
                                                                                                   +
                                                                                                   "jk!1")
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil)
                                                                                   ("2"
                                                                                    (hide-all-but
                                                                                     1)
                                                                                    (("2"
                                                                                      (lemma
                                                                                       "archimedean")
                                                                                      (("2"
                                                                                        (inst
                                                                                         -1
                                                                                         "delta!1/2")
                                                                                        (("2"
                                                                                          (skosimp*)
                                                                                          (("2"
                                                                                            (inst
                                                                                             +
                                                                                             "max(jj!1,n!1)")
                                                                                            (("2"
                                                                                              (expand
                                                                                               "max")
                                                                                              (("2"
                                                                                                (lift-if)
                                                                                                (("2"
                                                                                                  (ground)
                                                                                                  (("2"
                                                                                                    (case
                                                                                                     "1/jj!1 <= 1/n!1")
                                                                                                    (("1"
                                                                                                      (assert)
                                                                                                      nil
                                                                                                      nil)
                                                                                                     ("2"
                                                                                                      (cross-mult
                                                                                                       1)
                                                                                                      nil
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil)
                                                                                 ("2"
                                                                                  (hide
                                                                                   -1
                                                                                   -2
                                                                                   -3
                                                                                   -4
                                                                                   -5
                                                                                   -10
                                                                                   -11
                                                                                   2
                                                                                   3)
                                                                                  (("2"
                                                                                    (skosimp*)
                                                                                    (("2"
                                                                                      (replace
                                                                                       -2
                                                                                       *
                                                                                       rl)
                                                                                      (("2"
                                                                                        (assert)
                                                                                        (("2"
                                                                                          (replace
                                                                                           -3
                                                                                           *
                                                                                           rl)
                                                                                          (("2"
                                                                                            (hide
                                                                                             -2
                                                                                             -3)
                                                                                            (("2"
                                                                                              (assert)
                                                                                              (("2"
                                                                                                (case
                                                                                                 "(FORALL (A,B: (bounded_above?)): subset?(A,B) IMPLIES
                                                                                                                                                                                                                                                                                                   lub(A) <= lub(B))")
                                                                                                (("1"
                                                                                                  (inst?)
                                                                                                  (("1"
                                                                                                    (assert)
                                                                                                    (("1"
                                                                                                      (hide
                                                                                                       2)
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "subset?")
                                                                                                        (("1"
                                                                                                          (expand
                                                                                                           "member")
                                                                                                          (("1"
                                                                                                            (skosimp*)
                                                                                                            (("1"
                                                                                                              (inst
                                                                                                               +
                                                                                                               "j!1")
                                                                                                              (("1"
                                                                                                                (assert)
                                                                                                                nil
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil)
                                                                                                   ("2"
                                                                                                    (hide
                                                                                                     2)
                                                                                                    (("2"
                                                                                                      (prop)
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "nonempty?")
                                                                                                        (("1"
                                                                                                          (expand
                                                                                                           "empty?")
                                                                                                          (("1"
                                                                                                            (expand
                                                                                                             "member")
                                                                                                            (("1"
                                                                                                              (inst
                                                                                                               -1
                                                                                                               "XX!1(jj!1)")
                                                                                                              (("1"
                                                                                                                (inst
                                                                                                                 +
                                                                                                                 "jj!1")
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  nil
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil)
                                                                                                       ("2"
                                                                                                        (expand
                                                                                                         "bounded_above?")
                                                                                                        (("2"
                                                                                                          (inst
                                                                                                           +
                                                                                                           "b!1")
                                                                                                          (("2"
                                                                                                            (expand
                                                                                                             "upper_bound?")
                                                                                                            (("2"
                                                                                                              (skosimp*)
                                                                                                              (("2"
                                                                                                                (typepred
                                                                                                                 "s!2")
                                                                                                                (("2"
--> --------------------

--> maximum size reached

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

¤ Dauer der Verarbeitung: 0.59 Sekunden  (vorverarbeitet)  ¤





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