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Datei: complex_field.prf Sprache: Lisp

Original von: PVS^©

(complex_field
(fullset_is_field 0
  (fullset_is_field-2 nil 3408269025
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                                                                    (assert)
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                                                               ("nzx"
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                                                            (("8"
                                                              (lemma
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                                                               ("n0x"
                                                                "x!1"))
                                                              (("8"
                                                                (lemma
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                                                                 ("z"
                                                                  "1"
                                                                  "n0z"
                                                                  "x!1"))
                                                                (("8"
                                                                  (inst
                                                                   +
                                                                   "1/x!1")
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                                                                    (("1"
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    nil)
   ((field? const-decl "bool" field_def "algebra/")
    (ring_with_one? const-decl "bool" ring_with_one_def "algebra/")
    (complex_times_complex_is_complex application-judgement "complex"
     complex_types nil)
    (restrict const-decl "R" restrict nil)
    (right_distributive? const-decl "bool" operator_defs_more
     "algebra/")
    (group? const-decl "bool" group_def "algebra/")
    (monad? const-decl "bool" monad_def "algebra/")
    (commutative? const-decl "bool" operator_defs nil)
    (remove const-decl "set" sets nil)
    (member const-decl "bool" sets nil)
    (commutative_mult formula-decl nil number_fields nil)
    (closed_divides formula-decl nil complex_types nil)
    (nzcomplex nonempty-type-eq-decl nil complex_types nil)
    (div_cancel1 formula-decl nil number_fields_bis nil)
    (div_cancel2 formula-decl nil number_fields_bis nil)
    (x!1 skolem-const-decl "({y | 0 /= y})" complex_field nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum_div_nznum_is_nznum application-judgement "nznum"
     number_fields_bis nil)
    (complex_div_nzcomplex_is_complex application-judgement "complex"
     complex_types nil)
    (nzcomplex_div_nzcomplex_is_nzcomplex application-judgement
     "nzcomplex" complex_types nil)
    (inv_ne_0 formula-decl nil number_fields_bis nil)
    (set type-eq-decl nil sets nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (nznum_times_nznum_is_nznum judgement-tcc nil number_fields_bis
     nil)
    (/= const-decl "boolean" notequal nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number_fields_left_identity_mult formula-decl nil
     number_fields_bis nil)
    (associative_mult formula-decl nil number_fields nil)
    (inv_exists? const-decl "bool" group_def "algebra/")
    (minus_complex_is_complex application-judgement "complex"
     complex_types nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (TRUE const-decl "bool" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (complex nonempty-type-from-decl nil complex_types nil)
    (complex_pred const-decl "[number_field -> boolean]" complex_types
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_fields_negate_is_right_inverse formula-decl nil
     number_fields_bis nil)
    (star_closed? const-decl "bool" groupoid_def "algebra/")
    (identity? const-decl "bool" operator_defs nil)
    (associative? const-decl "bool" operator_defs nil)
    (complex_plus_complex_is_complex application-judgement "complex"
     complex_types nil)
    (monoid? const-decl "bool" monoid_def "algebra/")
    (abelian_group? const-decl "bool" group_def "algebra/")
    (left_distributive? const-decl "bool" operator_defs_more
     "algebra/")
    (ring? const-decl "bool" ring_def "algebra/")
    (division_ring? const-decl "bool" division_ring_def "algebra/")
    (fullset const-decl "set" sets nil))
   nil)
  (fullset_is_field-1 nil 3385139699
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                                                               ("x"
                                                                "x!1"))
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                                                          (rewrite
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                                                          (typepred
                                                           "x!1")
                                                          (("5"
                                                            (typepred
                                                             "y!1")
                                                            (("5"
                                                              (lemma
                                                               "nznum_times_nznum_is_nznum"
                                                               ("nzx"
                                                                "x!1"
                                                                "nzy"
                                                                "y!1"))
                                                              (("5"
                                                                (assert)
                                                                nil
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                                                          nil
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                                                        (("8"
                                                          (skosimp)
                                                          (("8"
                                                            (typepred
                                                             "x!1")
                                                            (("8"
                                                              (lemma
                                                               "inv_ne_0"
                                                               ("n0x"
                                                                "x!1"))
                                                              (("8"
                                                                (lemma
                                                                 "closed_divides"
                                                                 ("z"
                                                                  "1"
                                                                  "n0z"
                                                                  "x!1"))
                                                                (("1"
                                                                  (inst
                                                                   +
                                                                   "1/x!1")
                                                                  (("1"
                                                                    (rewrite
                                                                     "div_cancel1")
                                                                    (("1"
                                                                      (rewrite
                                                                       "div_cancel2")
                                                                      nil
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (assert)
                                                                    nil
                                                                    nil))
                                                                  nil)
                                                                 ("2"
                                                                  (lemma
                                                                   "real_complex"
                                                                   ("x"
                                                                    "1"))
                                                                  (("2"
                                                                    (propax)
                                                                    nil
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil)
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                                                        (skosimp)
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                                                          nil
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    nil)
   ((field? const-decl "bool" field_def "algebra/")
    (ring_with_one? const-decl "bool" ring_with_one_def "algebra/")
    (right_distributive? const-decl "bool" operator_defs_more
     "algebra/")
    (group? const-decl "bool" group_def "algebra/")
    (monad? const-decl "bool" monad_def "algebra/")
    (complex_plus_complex_is_complex application-judgement "complex"
     complex_types nil)
    (star_closed? const-decl "bool" groupoid_def "algebra/")
    (number_fields_negate_is_right_inverse formula-decl nil
     number_fields_bis nil)
    (complex_pred const-decl "[number_field -> boolean]" complex_types
     nil)
    (complex nonempty-type-from-decl nil complex_types nil)
    (minus_complex_is_complex application-judgement "complex"
     complex_types nil)
    (number_fields_left_identity_mult formula-decl nil
     number_fields_bis nil)
    (nznum_times_nznum_is_nznum judgement-tcc nil number_fields_bis
     nil)
    (inv_ne_0 formula-decl nil number_fields_bis nil)
    (real_complex formula-decl nil complex_types nil)
    (nznum_div_nznum_is_nznum application-judgement "nznum"
     number_fields_bis nil)
    (div_cancel2 formula-decl nil number_fields_bis nil)
    (div_cancel1 formula-decl nil number_fields_bis nil)
    (nzcomplex nonempty-type-eq-decl nil complex_types nil)
    (closed_divides formula-decl nil complex_types nil)
    (monoid? const-decl "bool" monoid_def "algebra/")
    (abelian_group? const-decl "bool" group_def "algebra/")
    (left_distributive? const-decl "bool" operator_defs_more
     "algebra/")
    (complex_times_complex_is_complex application-judgement "complex"
     complex_types nil)
    (ring? const-decl "bool" ring_def "algebra/")
    (division_ring? const-decl "bool" division_ring_def "algebra/"))
   shostak))
(IMP_field_TCC1 0
  (IMP_field_TCC1-1 nil 3385121716
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                                                              (("5"
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                                                                   "nznum_times_nznum_is_nznum"
                                                                   ("nzx"
                                                                    "x!1"
                                                                    "nzy"
                                                                    "y!1"))
                                                                  (("5"
                                                                    (assert)
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                                                              (rewrite
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                                                            (expand
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                                                            (("8"
                                                              (skosimp)
                                                              (("8"
                                                                (typepred
                                                                 "x!1")
                                                                (("8"
                                                                  (lemma
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                                                                   ("n0x"
                                                                    "x!1"))
                                                                  (("8"
                                                                    (inst
                                                                     +
                                                                     "1/x!1")
                                                                    (("1"
                                                                      (assert)
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                                                                        (rewrite
                                                                         "div_cancel1")
                                                                        (("1"
                                                                          (rewrite
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                                                                          nil))
                                                                        nil))
                                                                      nil)
                                                                     ("2"
                                                                      (assert)
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                                                                      nil))
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                                                            (("9"
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   ((field? const-decl "bool" field_def "algebra/")
    (ring_with_one? const-decl "bool" ring_with_one_def "algebra/")
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    (right_distributive? const-decl "bool" operator_defs_more
     "algebra/")
    (commutative? const-decl "bool" operator_defs nil)
    (group? const-decl "bool" group_def "algebra/")
    (monoid? const-decl "bool" monoid_def "algebra/")
    (associative? const-decl "bool" operator_defs nil)
    (member const-decl "bool" sets nil)
    (identity? const-decl "bool" operator_defs nil)
    (commutative_mult formula-decl nil number_fields nil)
    (nzcomplex_div_nzcomplex_is_nzcomplex application-judgement
     "nzcomplex" complex_types nil)
    (complex_div_nzcomplex_is_complex application-judgement "complex"
     complex_types nil)
    (nznum_div_nznum_is_nznum application-judgement "nznum"
     number_fields_bis nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (x!1 skolem-const-decl "({y | 0 /= y})" complex_field nil)
    (div_cancel1 formula-decl nil number_fields_bis nil)
    (div_cancel2 formula-decl nil number_fields_bis nil)
    (inv_ne_0 formula-decl nil number_fields_bis nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (set type-eq-decl nil sets nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (nznum_times_nznum_is_nznum judgement-tcc nil number_fields_bis
     nil)
    (/= const-decl "boolean" notequal nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number_fields_left_identity_mult formula-decl nil
     number_fields_bis nil)
    (associative_mult formula-decl nil number_fields nil)
    (inv_exists? const-decl "bool" group_def "algebra/")
    (minus_complex_is_complex application-judgement "complex"
     complex_types nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (TRUE const-decl "bool" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (complex nonempty-type-from-decl nil complex_types nil)
    (complex_pred const-decl "[number_field -> boolean]" complex_types
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_fields_negate_is_right_inverse formula-decl nil
     number_fields_bis nil)
    (star_closed? const-decl "bool" groupoid_def "algebra/")
    (monad? const-decl "bool" monad_def "algebra/")
    (remove const-decl "set" sets nil)
    (restrict const-decl "R" restrict nil)
    (complex_times_complex_is_complex application-judgement "complex"
     complex_types nil)
    (complex_plus_complex_is_complex application-judgement "complex"
     complex_types nil)
    (left_distributive? const-decl "bool" operator_defs_more
     "algebra/")
    (ring? const-decl "bool" ring_def "algebra/")
    (division_ring? const-decl "bool" division_ring_def "algebra/")
    (fullset const-decl "set" sets nil))
   nil)))

¤ Dauer der Verarbeitung: 0.31 Sekunden (vorverarbeitet) ¤

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