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Datei: Casting3.java   Sprache: Lisp

Original von: PVS©

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                        (("" (assert)
                          ((""
                            (lemma "both_sides_plus_gt1"
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                                     "F"
                                     "LAMBDA (x:posreal): x - 1 - ln(x)")
                                    ((""
                                      (name
                                       "G"
                                       "LAMBDA (x:posreal): ln(x) - (x-1)/x")
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                                          (case
                                           "FORALL (x: posreal): EXISTS (y: posreal): x /= y")
                                          (("1"
                                            (lemma "ln_derivable")
                                            (("1"
                                              (flatten -1)
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                                                (lemma
                                                 "const_derivable_fun[posreal]"
                                                 ("b" "1"))
                                                (("1"
                                                  (lemma
                                                   "identity_derivable_fun[posreal]")
                                                  (("1"
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                                                     "diff_derivable_fun[posreal]")
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                                                       "I[posreal]"
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                                                         -
                                                         "I[posreal] - const_fun(1)"
                                                         "ln")
                                                        (("1"
                                                          (lemma
                                                           "div_derivable_fun[posreal]"
                                                           ("f"
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                                                            "g"
                                                            "I[posreal]"))
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                                                             -
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                                                                                           ("ff"
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                                                                                                                              (("1"
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                                                                                                                                (("1"
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                                                                                                                                              (replace
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                                                                                                                                                 -2
                                                                                                                                                 rl)
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                                                                                                                                                          (("1"
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                                                                                                                                                             -2)
                                                                                                                                                            (("1"
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                                                                                                                                                              nil)
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                                                                                                                                                                  (("2"
                                                                                                                                                                    (lemma
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                                                                                                                                                                     ("x"
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                                                                                                                                                                      "y"
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                                                                                                                                                                    (("2"
                                                                                                                                                                      (split
                                                                                                                                                                       -1)
                                                                                                                                                                      (("1"
                                                                                                                                                                        (lemma
                                                                                                                                                                         "negreal_times_negreal_is_posreal"
                                                                                                                                                                         ("nx"
                                                                                                                                                                          "y!1-1"
                                                                                                                                                                          "ny"
                                                                                                                                                                          "y!1-1"))
                                                                                                                                                                        (("1"
                                                                                                                                                                          (lemma
                                                                                                                                                                           "both_sides_div_pos_gt1"
                                                                                                                                                                           ("x"
                                                                                                                                                                            "(y!1-1)*(y!1-1)"
                                                                                                                                                                            "y"
                                                                                                                                                                            "0"
                                                                                                                                                                            "pz"
                                                                                                                                                                            "y!1"))
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                                                                                                                                                                         ("2"
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                                                                                                                                                                          nil
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                                                                                                                                                                        (propax)
                                                                                                                                                                        nil
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                                                                                                                                                                       ("3"
                                                                                                                                                                        (lemma
                                                                                                                                                                         "posreal_times_posreal_is_posreal"
                                                                                                                                                                         ("px"
                                                                                                                                                                          "y!1-1"
                                                                                                                                                                          "py"
                                                                                                                                                                          "y!1-1"))
                                                                                                                                                                        (("1"
                                                                                                                                                                          (lemma
                                                                                                                                                                           "both_sides_div_pos_gt1"
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                                                                                                                                                                            "pz"
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                                                                                                                                                              (("2"
                                                                                                                                                                (rewrite
                                                                                                                                                                 "div_cancel1")
                                                                                                                                                                (("2"
                                                                                                                                                                  (lemma
                                                                                                                                                                   "div_times"
                                                                                                                                                                   ("x"
                                                                                                                                                                    "y!1"
                                                                                                                                                                    "n0x"
                                                                                                                                                                    "1"
                                                                                                                                                                    "y"
                                                                                                                                                                    "1"
                                                                                                                                                                    "n0y"
                                                                                                                                                                    "y!1*y!1"))
                                                                                                                                                                  (("2"
                                                                                                                                                                    (replace
                                                                                                                                                                     -1
                                                                                                                                                                     2)
                                                                                                                                                                    (("2"
                                                                                                                                                                      (simplify
                                                                                                                                                                       2)
                                                                                                                                                                      (("2"
                                                                                                                                                                        (simplify
                                                                                                                                                                         2)
                                                                                                                                                                        (("2"
                                                                                                                                                                          (lemma
                                                                                                                                                                           "div_cancel1"
                                                                                                                                                                           ("x"
                                                                                                                                                                            "1/y!1"
                                                                                                                                                                            "n0z"
                                                                                                                                                                            "y!1"))
                                                                                                                                                                          (("2"
                                                                                                                                                                            (rewrite
                                                                                                                                                                             "div_div2"
                                                                                                                                                                             -1)
                                                                                                                                                                            (("2"
                                                                                                                                                                              (replace
                                                                                                                                                                               -1)
                                                                                                                                                                              (("2"
                                                                                                                                                                                (hide
                                                                                                                                                                                 -1)
                                                                                                                                                                                (("2"
                                                                                                                                                                                  (lemma
                                                                                                                                                                                   "trich_lt"
                                                                                                                                                                                   ("x"
                                                                                                                                                                                    "y!1"
                                                                                                                                                                                    "y"
                                                                                                                                                                                    "1"))
                                                                                                                                                                                  (("2"
                                                                                                                                                                                    (split
                                                                                                                                                                                     -1)
                                                                                                                                                                                    (("1"
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                                                                                                                                                                                       "negreal_times_negreal_is_posreal"
                                                                                                                                                                                       ("nx"
                                                                                                                                                                                        "y!1-1"
                                                                                                                                                                                        "ny"
                                                                                                                                                                                        "y!1-1"))
                                                                                                                                                                                      (("1"
                                                                                                                                                                                        (lemma
                                                                                                                                                                                         "both_sides_div_pos_gt1"
                                                                                                                                                                                         ("pz"
                                                                                                                                                                                          "y!1*y!1"
                                                                                                                                                                                          "x"
                                                                                                                                                                                          "(y!1-1)*(y!1-1)"
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                                                                                                                                                                                          "0"))
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                                                                                                                                                                                        "py"
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                                                                                                                                                                                          "x"
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--> --------------------

--> maximum size reached

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

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