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Datei: continuity_ms_def.prf   Sprache: Lisp

Original von: PVS©

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                          (("1" (decompose-equality +)
                            (("1" (decompose-equality +)
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    (subset? const-decl "bool" sets nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
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    (Op_Pair type-eq-decl nil riesz_hahn_banach nil)
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    (Operator type-eq-decl nil riesz_linear_functionals nil)
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    (= const-decl "[T, T -> boolean]" equalities nil)
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    (reflexive? const-decl "bool" relations nil)
    (partial_order? const-decl "bool" orders nil))
   shostak))
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    (<= const-decl "bool" riesz_hahn_banach nil)
    (Op_Pair type-eq-decl nil riesz_hahn_banach nil)
    (bounded_linear_operator? const-decl "bool"
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    (Operator type-eq-decl nil riesz_linear_functionals nil)
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    (partial_order? const-decl "bool" orders nil))
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      (("" (name "OEnorm" "op_norm[a, b, ((OE`space))](OE`Lop)")
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                                          (("2"
                                            (assert)
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                                              (split +)
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                    (("2" (label "ExtExists" 2)
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                        (("1" (label "funchoosename" -1)
                          (("1"
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                                  "(LAMBDA (gg: (Extspace)):
                                                                                                                                                                                                                            choose({ffc: real |
                                                                                                                                                                                                                                      EXISTS (rr: [INTab->real]):
                                                                                                                                                                                                                                        OE`space(rr) AND gg = rr + ffc * ff}))")
                            (("1" (label "constchoosename" -1)
                              (("1"
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                                                        (("1"
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                                                            -
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                                                          (("1"
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                                                             (inst
                                                              -
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                                                              "(1 / (rr - constchoose(gg)))"))
                                                            (("1"
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                                                       ("2"
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                                                                 1)
                                                                (("2"
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                                                                   :exclude
                                                                   ("funchoose"
                                                                    "constchoose"))
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                                                              nil))
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                                  (("2"
                                    (case
                                     "NOT FORALL (gg:(Extspace), fq:(OE`space)): gg = fq + constchoose(gg)*ff IMPLIES fq = funchoose(gg)")
                                    (("1"
                                      (skeep)
                                      (("1"
                                        (typepred "funchoose(gg)")
                                        (("1"
                                          (skosimp*)
                                          (("1"
                                            (case
                                             "ffc!1 = constchoose(gg)")
                                            (("1"
                                              (replace -1)
                                              (("1"
                                                (hide-all-but
                                                 (-3 -4 1))
                                                (("1"
                                                  (decompose-equality
                                                   +)
                                                  (("1"
                                                    (decompose-equality
                                                     -)
                                                    (("1"
                                                      (decompose-equality
                                                       -)
                                                      (("1"
                                                        (inst - "x!1")
                                                        (("1"
                                                          (inst
                                                           -
                                                           "x!1")
                                                          (("1"
                                                            (grind
                                                             :exclude
                                                             ("funchoose"
                                                              "constchoose"))
                                                            nil
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("2"
                                              (case
                                               "ff = (1/(ffc!1-constchoose(gg)))*(fq+(-1)*funchoose(gg))")
                                              (("1"
                                                (typepred "OE`space")
                                                (("1"
                                                  (expand
                                                   "bounded_linear_subspace?"
                                                   -1)
                                                  (("1"
                                                    (flatten)
                                                    (("1"
                                                      (expand
                                                       "funs_const_closed?")
                                                      (("1"
                                                        (inst-cp
                                                         -
                                                         "funchoose(gg)"
                                                         "-1")
                                                        (("1"
                                                          (expand
                                                           "funs_sum_closed?")
                                                          (("1"
                                                            (step_assert
                                                             (inst
                                                              -
                                                              "fq"
                                                              "-1 * funchoose(gg)"))
                                                            (("1"
                                                              (step_assert
                                                               (inst
                                                                -
                                                                "fq + -1 * funchoose(gg)"
                                                                "(1 / (ffc!1 - constchoose(gg)))"))
                                                              (("1"
                                                                (assert)
                                                                nil
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)
                                               ("2"
                                                (hide-all-but
                                                 (-2 -3 1))
                                                (("2"
                                                  (decompose-equality
                                                   +)
                                                  (("2"
                                                    (decompose-equality
                                                     -)
                                                    (("2"
                                                      (decompose-equality
                                                       -)
                                                      (("2"
                                                        (inst - "x!1")
                                                        (("2"
                                                          (inst
                                                           -
                                                           "x!1")
                                                          (("2"
                                                            (replace
                                                             -1)
                                                            (("2"
                                                              (hide -1)
                                                              (("2"
                                                                (expand
                                                                 "*")
                                                                (("2"
                                                                  (cross-mult
                                                                   1)
                                                                  (("2"
                                                                    (assert)
                                                                    (("2"
                                                                      (grind
                                                                       :exclude
                                                                       ("funchoose"
                                                                        "constchoose"))
                                                                      nil
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)
                                               ("3" (assertnil nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (label "funchooseunique2" -1)
                                      (("2"
                                        (case
                                         "NOT FORALL (gg:(Extspace)): gg = funchoose(gg) + constchoose(gg)*ff")
                                        (("1"
                                          (skeep)
                                          (("1"
                                            (typepred
                                             "constchoose(gg)")
                                            (("1"
                                              (skosimp*)
                                              (("1"
                                                (inst
                                                 "funchooseunique2"
                                                 "gg"
                                                 "rr!1")
                                                (("1"
                                                  (assert)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (label "ggdecomp" -1)
                                          (("2"
                                            (case
                                             "NOT FORALL (gg: (Extspace), fq: (OE`space), rr:real):
                                                                                                                                        gg = fq + rr * ff IMPLIES fq = funchoose(gg) AND rr = constchoose(gg)")
                                            (("1"
                                              (skeep)
                                              (("1"
                                                (case
                                                 "rr = constchoose(gg)")
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (inst
                                                     "funchooseunique2"
                                                     "gg"
                                                     "fq")
                                                    (("1"
                                                      (assert)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (hide 2)
                                                  (("2"
                                                    (inst
                                                     "ggdecomp"
                                                     "gg")
                                                    (("2"
                                                      (case
                                                       "ff = (1/(rr-constchoose(gg)))*(funchoose(gg)+(-1)*fq)")
                                                      (("1"
                                                        (typepred
                                                         "OE`space")
                                                        (("1"
                                                          (expand
                                                           "bounded_linear_subspace?"
                                                           -1)
                                                          (("1"
                                                            (flatten)
                                                            (("1"
                                                              (expand
                                                               "funs_const_closed?")
                                                              (("1"
                                                                (inst-cp
                                                                 -
                                                                 "fq"
                                                                 "-1")
                                                                (("1"
                                                                  (expand
                                                                   "funs_sum_closed?")
                                                                  (("1"
                                                                    (step_assert
                                                                     (inst
                                                                      -
                                                                      "funchoose(gg)"
                                                                      "(-1)*fq"))
                                                                    (("1"
                                                                      (step_assert
                                                                       (inst
                                                                        -
                                                                        "funchoose(gg) + (-1) * fq"
                                                                        "(1 / (rr - constchoose(gg)))"))
                                                                      (("1"
                                                                        (assert)
                                                                        nil
                                                                        nil))
--> --------------------

--> maximum size reached

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

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