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Datei: cross_metric_uniform_continuity.pvs   Sprache: Lisp

Original von: PVS©

(cross_metric_uniform_continuity
 (IMP_cross_metric_spaces_TCC1 0
  (IMP_cross_metric_spaces_TCC1-1 nil 3460217227
   ("" (lemma "fullset_metric_space1") (("" (propax) nil nil)) nil)
   ((fullset_metric_space1 formula-decl nil
     cross_metric_uniform_continuity nil))
   nil))
 (IMP_cross_metric_spaces_TCC2 0
  (IMP_cross_metric_spaces_TCC2-1 nil 3460217227
   ("" (lemma "fullset_metric_space2") (("" (propax) nil nil)) nil)
   ((fullset_metric_space2 formula-decl nil
     cross_metric_uniform_continuity nil))
   nil))
 (IMP_continuity_ms_def_TCC1 0
  (IMP_continuity_ms_def_TCC1-1 nil 3460217227
   ("" (lemma "product_is_metric") (("" (propax) nil nil)) nil)
   ((product_is_metric formula-decl nil cross_metric_spaces nil)
    (T1 formal-nonempty-type-decl nil cross_metric_uniform_continuity
     nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nnreal type-eq-decl nil real_types nil)
    (d1 formal-const-decl "[T1, T1 -> nnreal]"
     cross_metric_uniform_continuity nil)
    (T2 formal-nonempty-type-decl nil cross_metric_uniform_continuity
     nil)
    (d2 formal-const-decl "[T2, T2 -> nnreal]"
     cross_metric_uniform_continuity nil))
   nil))
 (IMP_continuity_ms_def_TCC2 0
  (IMP_continuity_ms_def_TCC2-1 nil 3460217227
   ("" (lemma "fullset_metric_space3") (("" (propax) nil nil)) nil)
   ((fullset_metric_space3 formula-decl nil
     cross_metric_uniform_continuity nil))
   nil))
 (multiary_Heine 0
  (multiary_Heine-2 nil 3565651140
   ("" (skosimp*)
    (("" (label "comp" -1)
      (("" (label "cont" -2)
        (("" (label "unif" 1)
          (("" (lemma "one_variable_unif_cont_sequence")
            (("" (label "epsq" -1)
              (("" (inst "epsq" "X!1" "Y!1" "f!1")
                (("" (assert)
                  (("" (skosimp*)
                    (("" (lemma "compact_sequence_limit[T1,d1]")
                      (("" (label "csl" -1)
                        (("" (inst "csl" "X!1")
                          (("" (assert)
                            (("" (prop)
                              (("1"
                                (inst
                                 "csl"
                                 "(LAMBDA (n: nat): IF n = 0 THEN seq!1(1)`1 ELSE seq!1(n)`1 ENDIF)")
                                (("1"
                                  (skosimp*)
                                  (("1"
                                    (lemma
                                     "product_cont_product_subset")
                                    (("1"
                                      (label "pcps" -1)
                                      (("1"
                                        (inst "pcps" "X!1" "Y!1" "f!1")
                                        (("1"
                                          (assert)
                                          (("1"
                                            (inst
                                             "pcps"
                                             "p!1"
                                             "y!1"
                                             "epsilon!1/2")
                                            (("1"
                                              (skosimp*)
                                              (("1"
                                                (lemma "archimedean")
                                                (("1"
                                                  (label "arch" -1)
                                                  (("1"
                                                    (inst
                                                     "arch"
                                                     "delta!1/2")
                                                    (("1"
                                                      (skosimp *)
                                                      (("1"
                                                        (inst
                                                         "csl"
                                                         "1/n!1"
                                                         "n!1")
                                                        (("1"
                                                          (skosimp*)
                                                          (("1"
                                                            (typepred
                                                             "n!2")
                                                            (("1"
                                                              (label
                                                               "n!2T"
                                                               -1)
                                                              (("1"
                                                                (lemma
                                                                 "fullset_metric_space1")
                                                                (("1"
                                                                  (expand
                                                                   "metric_space?")
                                                                  (("1"
                                                                    (prop)
                                                                    (("1"
                                                                      (label
                                                                       "sz1"
                                                                       -1)
                                                                      (("1"
                                                                        (label
                                                                         "sym1"
                                                                         -2)
                                                                        (("1"
                                                                          (label
                                                                           "tri1"
                                                                           -3)
                                                                          (("1"
                                                                            (lemma
                                                                             "fullset_metric_space3")
                                                                            (("1"
                                                                              (expand
                                                                               "metric_space?")
                                                                              (("1"
                                                                                (prop)
                                                                                (("1"
                                                                                  (label
                                                                                   "sz3"
                                                                                   -1)
                                                                                  (("1"
                                                                                    (label
                                                                                     "sym3"
                                                                                     -2)
                                                                                    (("1"
                                                                                      (label
                                                                                       "tri3"
                                                                                       -3)
                                                                                      (("1"
                                                                                        (expand
                                                                                         "space_symmetric?")
                                                                                        (("1"
                                                                                          (expand
                                                                                           "space_triangle?")
                                                                                          (("1"
                                                                                            (hide
                                                                                             "sz1"
                                                                                             "sz3")
                                                                                            (("1"
                                                                                              (lemma
                                                                                               "fullset_metric_space2")
                                                                                              (("1"
                                                                                                (expand
                                                                                                 "metric_space?")
                                                                                                (("1"
                                                                                                  (prop)
                                                                                                  (("1"
                                                                                                    (hide
                                                                                                     -2
                                                                                                     -3)
                                                                                                    (("1"
                                                                                                      (label
                                                                                                       "sz2"
                                                                                                       -1)
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "space_zero?")
                                                                                                        (("1"
                                                                                                          (copy
                                                                                                           "tri1")
                                                                                                          (("1"
                                                                                                            (hide
                                                                                                             "tri1")
                                                                                                            (("1"
                                                                                                              (inst-cp
                                                                                                               -1
                                                                                                               "seq!1(n!2)`2"
                                                                                                               "seq!1(n!2)`1"
                                                                                                               "p!1")
                                                                                                              (("1"
                                                                                                                (label
                                                                                                                 "tri1a"
                                                                                                                 -1)
                                                                                                                (("1"
                                                                                                                  (label
                                                                                                                   "tri1inst"
                                                                                                                   -2)
                                                                                                                  (("1"
                                                                                                                    (inst
                                                                                                                     "epsq"
                                                                                                                     "n!2")
                                                                                                                    (("1"
                                                                                                                      (copy
                                                                                                                       "epsq")
                                                                                                                      (("1"
                                                                                                                        (hide
                                                                                                                         "epsq")
                                                                                                                        (("1"
                                                                                                                          (prop)
                                                                                                                          (("1"
                                                                                                                            (label
                                                                                                                             "mbs1"
                                                                                                                             -1)
                                                                                                                            (("1"
                                                                                                                              (label
                                                                                                                               "mbs2"
                                                                                                                               -2)
                                                                                                                              (("1"
                                                                                                                                (label
                                                                                                                                 "mbs3"
                                                                                                                                 -3)
                                                                                                                                (("1"
                                                                                                                                  (hide
                                                                                                                                   "mbs1"
                                                                                                                                   "mbs2"
                                                                                                                                   "mbs3")
                                                                                                                                  (("1"
                                                                                                                                    (label
                                                                                                                                     "s12lt"
                                                                                                                                     -1)
                                                                                                                                    (("1"
                                                                                                                                      (label
                                                                                                                                       "s3ylt"
                                                                                                                                       -2)
                                                                                                                                      (("1"
                                                                                                                                        (label
                                                                                                                                         "d3gt"
                                                                                                                                         -3)
                                                                                                                                        (("1"
                                                                                                                                          (copy
                                                                                                                                           "csl")
                                                                                                                                          (("1"
                                                                                                                                            (label
                                                                                                                                             "cls2"
                                                                                                                                             -1)
                                                                                                                                            (("1"
                                                                                                                                              (copy
                                                                                                                                               "sym1")
                                                                                                                                              (("1"
                                                                                                                                                (inst
                                                                                                                                                 -1
                                                                                                                                                 "seq!1(n!2)`1"
                                                                                                                                                 "seq!1(n!2)`2")
                                                                                                                                                (("1"
                                                                                                                                                  (replace
                                                                                                                                                   -1
                                                                                                                                                   "s12lt")
                                                                                                                                                  (("1"
                                                                                                                                                    (hide
                                                                                                                                                     -1)
                                                                                                                                                    (("1"
                                                                                                                                                      (copy
                                                                                                                                                       "cls2")
                                                                                                                                                      (("1"
                                                                                                                                                        (label
                                                                                                                                                         "cls3"
                                                                                                                                                         -1)
                                                                                                                                                        (("1"
                                                                                                                                                          (add-formulas
                                                                                                                                                           "s12lt"
                                                                                                                                                           "cls3")
                                                                                                                                                          (("1"
                                                                                                                                                            (label
                                                                                                                                                             "tri_inst1"
                                                                                                                                                             -1)
                                                                                                                                                            (("1"
                                                                                                                                                              (add-formulas
                                                                                                                                                               "tri_inst1"
                                                                                                                                                               "tri1inst")
                                                                                                                                                              (("1"
                                                                                                                                                                (label
                                                                                                                                                                 "tri_inst2"
                                                                                                                                                                 -1)
                                                                                                                                                                (("1"
                                                                                                                                                                  (both-sides
                                                                                                                                                                   "-"
                                                                                                                                                                   "d1(seq!1(n!2)`1, p!1) + d1(seq!1(n!2)`2, seq!1(n!2)`1)"
                                                                                                                                                                   "tri_inst2")
                                                                                                                                                                  (("1"
                                                                                                                                                                    (assert)
                                                                                                                                                                    (("1"
                                                                                                                                                                      (copy
                                                                                                                                                                       "arch")
                                                                                                                                                                      (("1"
                                                                                                                                                                        (label
                                                                                                                                                                         "arch2"
                                                                                                                                                                         -1)
                                                                                                                                                                        (("1"
                                                                                                                                                                          (add-formulas
                                                                                                                                                                           "arch2"
                                                                                                                                                                           "arch2")
                                                                                                                                                                          (("1"
                                                                                                                                                                            (add-formulas
                                                                                                                                                                             -1
                                                                                                                                                                             "tri_inst2")
                                                                                                                                                                            (("1"
                                                                                                                                                                              (assert)
                                                                                                                                                                              (("1"
                                                                                                                                                                                (lemma
                                                                                                                                                                                 "both_sides_div_pos_lt2")
                                                                                                                                                                                (("1"
                                                                                                                                                                                  (label
                                                                                                                                                                                   "both_sides_div_pos_lt2"
                                                                                                                                                                                   -1)
                                                                                                                                                                                  (("1"
                                                                                                                                                                                    (inst
                                                                                                                                                                                     "both_sides_div_pos_lt2"
                                                                                                                                                                                     "n!2"
                                                                                                                                                                                     "n!1"
                                                                                                                                                                                     "1")
                                                                                                                                                                                    (("1"
                                                                                                                                                                                      (prop)
                                                                                                                                                                                      (("1"
                                                                                                                                                                                        (hide
                                                                                                                                                                                         -2)
                                                                                                                                                                                        (("1"
                                                                                                                                                                                          (add-formulas
                                                                                                                                                                                           -1
                                                                                                                                                                                           -2)
                                                                                                                                                                                          (("1"
                                                                                                                                                                                            (both-sides
                                                                                                                                                                                             "-"
                                                                                                                                                                                             "2 * (1 / n!1) + 1 / n!2"
                                                                                                                                                                                             -1)
                                                                                                                                                                                            (("1"
                                                                                                                                                                                              (assert)
                                                                                                                                                                                              (("1"
                                                                                                                                                                                                (label
                                                                                                                                                                                                 "d1sp1"
                                                                                                                                                                                                 -1)
                                                                                                                                                                                                (("1"
                                                                                                                                                                                                  (copy
                                                                                                                                                                                                   "pcps")
                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                    (hide
                                                                                                                                                                                                     "pcps")
                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                      (label
                                                                                                                                                                                                       "pcps2"
                                                                                                                                                                                                       -1)
                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                        (copy
                                                                                                                                                                                                         "pcps2")
                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                          (label
                                                                                                                                                                                                           "pcps3"
                                                                                                                                                                                                           -1)
                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                            (inst
                                                                                                                                                                                                             "pcps3"
                                                                                                                                                                                                             "seq!1(n!2)`2"
                                                                                                                                                                                                             "seq!1(n!2)`3")
                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                              (prop)
                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                (inst
                                                                                                                                                                                                                 "pcps2"
                                                                                                                                                                                                                 "seq!1(n!2)`1"
                                                                                                                                                                                                                 "y!1")
                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                  (inst
                                                                                                                                                                                                                   "sym1"
                                                                                                                                                                                                                   "p!1"
                                                                                                                                                                                                                   "seq!1(n!2)`1")
                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                    (replace
                                                                                                                                                                                                                     "sym1")
                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                      (inst
                                                                                                                                                                                                                       "sz2"
                                                                                                                                                                                                                       "y!1"
                                                                                                                                                                                                                       "y!1")
                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                        (copy
                                                                                                                                                                                                                         "arch")
                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                          (label
                                                                                                                                                                                                                           "arch3"
                                                                                                                                                                                                                           -1)
                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                            (add-formulas
                                                                                                                                                                                                                             "cls2"
                                                                                                                                                                                                                             "arch")
                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                              (assert)
                                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                                (assert)
                                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                                  (both-sides
                                                                                                                                                                                                                                   "-"
                                                                                                                                                                                                                                   "1/n!1"
                                                                                                                                                                                                                                   -1)
                                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                                    (assert)
                                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                                      (inst
                                                                                                                                                                                                                                       "tri3"
                                                                                                                                                                                                                                       "f!1(seq!1(n!2)`1,y!1)"
                                                                                                                                                                                                                                       "f!1(p!1,y!1)"
                                                                                                                                                                                                                                       "f!1(seq!1(n!2)`2, seq!1(n!2)`3)")
                                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                                        (hide-all-but
                                                                                                                                                                                                                                         ("pcps3"
                                                                                                                                                                                                                                          "pcps2"
                                                                                                                                                                                                                                          "tri3"
                                                                                                                                                                                                                                          "sym3"
                                                                                                                                                                                                                                          "d3gt"
                                                                                                                                                                                                                                          "arch3"))
                                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                                          (inst
                                                                                                                                                                                                                                           "sym3"
                                                                                                                                                                                                                                           "f!1(seq!1(n!2)`1, y!1)"
                                                                                                                                                                                                                                           "f!1(p!1, y!1)")
                                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                                            (replace
                                                                                                                                                                                                                                             "sym3")
                                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                                              (add-formulas
                                                                                                                                                                                                                                               "tri3"
                                                                                                                                                                                                                                               "pcps3")
                                                                                                                                                                                                                                              nil
                                                                                                                                                                                                                                              nil))
                                                                                                                                                                                                                                            nil)
                                                                                                                                                                                                                                           ("2"
                                                                                                                                                                                                                                            (expand
                                                                                                                                                                                                                                             "fullset")
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                                                                                                                                                                                                                                              (propax)
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                                                                                                                                                                                                                                              nil))
                                                                                                                                                                                                                                            nil)
                                                                                                                                                                                                                                           ("3"
                                                                                                                                                                                                                                            (expand
                                                                                                                                                                                                                                             "fullset")
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                                                                                                                                                                                                                                              (propax)
                                                                                                                                                                                                                                              nil
                                                                                                                                                                                                                                              nil))
                                                                                                                                                                                                                                            nil))
                                                                                                                                                                                                                                          nil))
                                                                                                                                                                                                                                        nil)
                                                                                                                                                                                                                                       ("2"
                                                                                                                                                                                                                                        (expand
                                                                                                                                                                                                                                         "fullset")
                                                                                                                                                                                                                                        (("2"
                                                                                                                                                                                                                                          (propax)
                                                                                                                                                                                                                                          nil
                                                                                                                                                                                                                                          nil))
                                                                                                                                                                                                                                        nil)
                                                                                                                                                                                                                                       ("3"
                                                                                                                                                                                                                                        (expand
                                                                                                                                                                                                                                         "fullset")
                                                                                                                                                                                                                                        (("3"
                                                                                                                                                                                                                                          (propax)
--> --------------------

--> maximum size reached

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

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