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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: ppvernac.ml   Sprache: Lisp

Original von: PVS©

(vs_only
 (vs_only_TCC1 0
  (vs_only_TCC1-2 nil 3465560929
   ("" (skeep)
    (("" (assert)
      (("" (lemma "Delta_gt_0_nzv")
        (("" (inst?) (("" (assertnil nil)) nil)) nil))
      nil))
    nil)
   ((sq_nz_pos application-judgement "posreal" sq "reals/")
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (vect2 const-decl "Vect2" vect_3D_2D "vectors/")
    (Vect3 type-eq-decl nil vectors_3D_def "vectors/")
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (Delta_gt_0_nzv formula-decl nil horizontal 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)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (D formal-const-decl "posreal" vs_only nil))
   nil)
  (vs_only_TCC1-1 nil 3451819894
   ("" (skeep) (("" (assertnil nil)) nil)
   ((sq_nz_pos application-judgement "posreal" sq "reals/")) nil))
 (vs_only_TCC2 0
  (vs_only_TCC2-2 nil 3465683789
   ("" (skeep)
    (("" (lemma "Theta_D_neq_0")
      (("" (inst?) (("" (assertnil nil)) nil)) nil))
    nil)
   ((D formal-const-decl "posreal" vs_only nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (Theta_D_neq_0 formula-decl nil horizontal nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (Ss_vect2 type-eq-decl nil horizontal nil)
    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (zero const-decl "Vector" vectors_2D "vectors/")
    (Sign type-eq-decl nil sign "reals/")
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (nzint nonempty-type-eq-decl nil integers nil)
    (/= const-decl "boolean" notequal nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (nnreal type-eq-decl nil real_types nil)
    (sqv const-decl "nnreal" vectors_2D "vectors/")
    (Vect3 type-eq-decl nil vectors_3D_def "vectors/")
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (vect2 const-decl "Vect2" vect_3D_2D "vectors/")
    (s skolem-const-decl "Vect3" vs_only nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (sq_nz_pos application-judgement "posreal" sq "reals/"))
   nil)
  (vs_only_TCC2-1 nil 3465683704 ("" (subtype-tcc) nil nilnil nil))
 (vs_only_TCC3 0
  (vs_only_TCC3-1 nil 3466271452 ("" (subtype-tcc) nil nil)
   ((real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nzint nonempty-type-eq-decl nil integers nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (Sign type-eq-decl nil sign "reals/")
    (vect2 const-decl "Vect2" vect_3D_2D "vectors/")
    (* const-decl "real" vectors_2D "vectors/")
    (sqv const-decl "nnreal" vectors_2D "vectors/")
    (sq const-decl "nonneg_real" sq "reals/")
    (det const-decl "real" det_2D "vectors/")
    (D formal-const-decl "posreal" vs_only nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (Delta const-decl "real" horizontal nil)
    (/= const-decl "boolean" notequal nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil))
   nil))
 (circle_vs_only_ge 0
  (circle_vs_only_ge-2 nil 3470157239
   ("" (skeep)
    (("" (expand "circle_criterion?")
      (("" (flatten)
        (("" (rewrite "vect2_add")
          (("" (rewrite "vect2_add")
            (("" (rewrite "vect2_scal")
              (("" (rewrite "vect2_scal")
                (("" (assert)
                  (("" (lemma "vertical_sep_dir_at")
                    (("" (inst -1 "-eps" "nnt" "v`z" "s`z" "vz")
                      (("" (assert)
                        (("" (hide -2 -4)
                          (("" (expand"+" "*")
                            (("" (ground) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((sign_neg_clos application-judgement "Sign" sign "reals/")
    (real_times_real_is_real application-judgement "real" reals nil)
    (circle_criterion? const-decl "bool" circle_criterion nil)
    (vect2_add formula-decl nil vect_3D_2D "vectors/")
    (real nonempty-type-from-decl nil reals nil)
    (Vect3 type-eq-decl nil vectors_3D_def "vectors/")
    (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)
    (Vector type-eq-decl nil vectors_3D "vectors/")
    (* const-decl "Vector" vectors_3D "vectors/")
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nnreal type-eq-decl nil real_types nil)
    (vect2_scal formula-decl nil vect_3D_2D "vectors/")
    (vect2_eq formula-decl nil vect_3D_2D "vectors/")
    (real_plus_real_is_real application-judgement "real" reals nil)
    (sq_nz_pos application-judgement "posreal" sq "reals/")
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (Sign type-eq-decl nil sign "reals/")
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (nzint nonempty-type-eq-decl nil integers nil)
    (/= const-decl "boolean" notequal nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (+ const-decl "Vector" vectors_3D "vectors/")
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (H formal-const-decl "posreal" vs_only nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (vertical_sep_dir_at formula-decl nil vz_criteria nil))
   nil)
  (circle_vs_only_ge-1 nil 3451818153
   ("" (skeep)
    (("" (expand "circle_criterion?")
      (("" (flatten)
        (("" (rewrite "vect2_add")
          (("" (rewrite "vect2_scal") (("" (assertnil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((sign_neg_clos application-judgement "Sign" sign "reals/")
    (vect2_add formula-decl nil vect_3D_2D "vectors/")
    (Vect3 type-eq-decl nil vectors_3D_def "vectors/")
    (Vector type-eq-decl nil vectors_3D "vectors/")
    (* const-decl "Vector" vectors_3D "vectors/")
    (sq_nz_pos application-judgement "posreal" sq "reals/")
    (vect2_scal formula-decl nil vect_3D_2D "vectors/"))
   nil))
 (vs_entry_meets_circle_criterion_TCC1 0
  (vs_entry_meets_circle_criterion_TCC1-2 nil 3471099308
   ("" (skeep)
    (("" (rewrite "horizontal_conflict")
      (("" (flatten) (("" (assertnil nil)) nil)) nil))
    nil)
   ((nzv2 application-judgement "Nz_vect2" definitions_3D nil)
    (horizontal_conflict formula-decl nil horizontal nil)
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (/= const-decl "boolean" notequal nil)
    (zero const-decl "Vector" vectors_2D "vectors/")
    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (Vect3 type-eq-decl nil vectors_3D_def "vectors/")
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (vect2 const-decl "Vect2" vect_3D_2D "vectors/")
    (Nzv2_vect3 type-eq-decl nil definitions_3D nil)
    (nnreal type-eq-decl nil real_types nil)
    (sqv const-decl "nnreal" vectors_2D "vectors/")
    (sq const-decl "nonneg_real" sq "reals/")
    (H formal-const-decl "posreal" vs_only nil)
    (Ss2_vect3 type-eq-decl nil space_3D 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)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (D formal-const-decl "posreal" vs_only nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (sq_nz_pos application-judgement "posreal" sq "reals/")
    (nz_sqv_gt_0 application-judgement "posreal" vectors_2D "vectors/")
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (ssv2 application-judgement "Ss_vect2[D]" vs_only nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil)
  (vs_entry_meets_circle_criterion_TCC1-1 nil 3471099160
   ("" (subtype-tcc) nil nilnil nil))
 (vs_entry_meets_circle_criterion_TCC2 0
  (vs_entry_meets_circle_criterion_TCC2-2 nil 3471099331
   ("" (skeep)
    (("" (lemma "Theta_D_entry_gt_0")
      (("" (inst?) (("" (assertnil nil)) nil)) nil))
    nil)
   ((D formal-const-decl "posreal" vs_only nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (Theta_D_entry_gt_0 formula-decl nil horizontal nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (Ss2_vect3 type-eq-decl nil space_3D nil)
    (H formal-const-decl "posreal" vs_only nil)
    (Ss_vect2 type-eq-decl nil horizontal nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (sqv const-decl "nnreal" vectors_2D "vectors/")
    (nnreal type-eq-decl nil real_types nil)
    (Nzv2_vect3 type-eq-decl nil definitions_3D nil)
    (vect2 const-decl "Vect2" vect_3D_2D "vectors/")
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (Vect3 type-eq-decl nil vectors_3D_def "vectors/")
    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (zero const-decl "Vector" vectors_2D "vectors/")
    (/= const-decl "boolean" notequal nil)
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (nzv2 application-judgement "Nz_vect2" definitions_3D nil)
    (ssv2 application-judgement "Ss_vect2[D]" vs_only nil))
   nil)
  (vs_entry_meets_circle_criterion_TCC2-1 nil 3471099160
   ("" (subtype-tcc) nil nilnil nil))
 (vs_entry_meets_circle_criterion 0
  (vs_entry_meets_circle_criterion-1 nil 3471099160
   ("" (skeep)
    (("" (lemma "horizontal_conflict")
      (("" (inst?)
        (("" (assert)
          (("" (flatten)
            (("" (lemma "Theta_D_entry_gt_0")
              (("" (inst?)
                (("" (assert)
                  ((""
                    (name-replace "tentry" "Theta_D(ss,vgs,Entry)"
                     :hide? nil)
                    (("" (lemma "circle_vs_only_ge")
                      ((""
                        (inst -1 "Entry" "tentry" "ss" "vgs"
                         "vs_at(ss`z, tentry, eps)")
                        (("1" (skoletin -1)
                          (("1" (assert)
                            (("1" (hide 2)
                              (("1"
                                (lemma "vs_at_H")
                                (("1"
                                  (inst?)
                                  (("1"
                                    (expand "circle_criterion?")
                                    (("1"
                                      (rewrite "vect2_add")
                                      (("1"
                                        (rewrite "vect2_scal")
                                        (("1"
                                          (case-replace
                                           "(ss + tentry * (vgs WITH [z := vs_at(ss`z, tentry, eps)]))`z =
         ss`z+tentry*vs_at(ss`z,tentry,eps)")
                                          (("1"
                                            (hide -1)
                                            (("1"
                                              (replaces -1)
                                              (("1"
                                                (lemma "Theta_D_on_D")
                                                (("1"
                                                  (inst?)
                                                  (("1"
                                                    (assert)
                                                    (("1"
                                                      (lemma
                                                       "sdotv_lt_0")
                                                      (("1"
                                                        (inst? -1)
                                                        (("1"
                                                          (rewrite
                                                           "horizontal_conflict_entry")
                                                          (("1"
                                                            (assert)
                                                            (("1"
                                                              (rewrite
                                                               "sign_abs")
                                                              (("1"
                                                                (lemma
                                                                 "sign_mult_pos")
                                                                (("1"
                                                                  (inst
                                                                   -1
                                                                   "H"
                                                                   "eps")
                                                                  (("1"
                                                                    (assert)
                                                                    (("1"
                                                                      (replaces
                                                                       -1)
                                                                      (("1"
                                                                        (rewrite
                                                                         "sign_id")
                                                                        (("1"
                                                                          (assert)
                                                                          (("1"
                                                                            (case-replace
                                                                             "eps*(eps*H) = H"
                                                                             :hide?
                                                                             nil)
                                                                            (("1"
                                                                              (assert)
                                                                              (("1"
                                                                                (expand
                                                                                 "vs_at")
                                                                                (("1"
                                                                                  (hide-all-but
                                                                                   (-1
                                                                                    -6
                                                                                    -10
                                                                                    -11
                                                                                    1))
                                                                                  (("1"
                                                                                    (grind-reals)
                                                                                    (("1"
                                                                                      (cancel-by
                                                                                       1
                                                                                       "H")
                                                                                      nil
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
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   ((D formal-const-decl "posreal" vs_only nil)
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    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
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    (real_pred const-decl "[number_field -> boolean]" reals nil)
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    (nz_sqv_gt_0 application-judgement "posreal" vectors_2D "vectors/")
    (real_gt_is_strict_total_order name-judgement
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    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
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    (real_times_real_is_real application-judgement "real" reals nil)
    (real_lt_is_strict_total_order name-judgement
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    (ssv2 application-judgement "Ss_vect2[D]" vs_only nil)
    (Theta_D_entry_gt_0 formula-decl nil horizontal nil)
    (circle_vs_only_ge formula-decl nil vs_only nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (IFF const-decl "[bool, bool -> bool]" booleans nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (sign const-decl "Sign" sign "reals/")
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (circle_criterion? const-decl "bool" circle_criterion nil)
    (Vector type-eq-decl nil vectors_3D "vectors/")
    (+ const-decl "Vector" vectors_3D "vectors/")
    (* const-decl "Vector" vectors_3D "vectors/")
    (<= const-decl "bool" reals nil)
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    (nzreal_times_nzreal_is_nzreal application-judgement "nzreal"
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    (sign_abs formula-decl nil sign "reals/")
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
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    (TRUE const-decl "bool" booleans nil)
    (id const-decl "(bijective?[T, T])" identity nil)
    (bijective? const-decl "bool" functions nil)
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    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
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    (posreal_div_posreal_is_posreal application-judgement "posreal"
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    (posreal_times_posreal_is_posreal application-judgement "posreal"
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    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (times_div2 formula-decl nil real_props nil)
    (times_div1 formula-decl nil real_props nil)
    (zero_times1 formula-decl nil real_props nil)
    (div_mult_pos_ge1 formula-decl nil real_props nil)
    (div_mult_pos_ge2 formula-decl nil real_props nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (sign_id formula-decl nil sign "reals/")
    (sign_mult_pos formula-decl nil sign "reals/")
    (Sp_vect2 type-eq-decl nil horizontal nil)
    (+ const-decl "Vector" vectors_2D "vectors/")
    (* const-decl "Vector" vectors_2D "vectors/")
    (nonzero_abs_is_pos application-judgement "{y: posreal | y >= x}"
     real_defs nil)
    (Theta_D_on_D formula-decl nil horizontal nil)
    (vect2_eq formula-decl nil vect_3D_2D "vectors/")
    (vect2_scal formula-decl nil vect_3D_2D "vectors/")
    (vs_at_H formula-decl nil vertical nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
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    (nzreal nonempty-type-eq-decl nil reals nil)
    (vs_at const-decl "real" vertical nil)
    (tentry skolem-const-decl "real" vs_only nil)
    (Theta_D const-decl "real" horizontal nil)
    (Sign type-eq-decl nil sign "reals/")
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (nzint nonempty-type-eq-decl nil integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (Delta const-decl "real" horizontal nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (Ss_vect2 type-eq-decl nil horizontal nil)
    (Ss2_vect3 type-eq-decl nil space_3D nil)
    (H formal-const-decl "posreal" vs_only nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (sqv const-decl "nnreal" vectors_2D "vectors/")
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    (Nzv2_vect3 type-eq-decl nil definitions_3D nil)
    (vect2 const-decl "Vect2" vect_3D_2D "vectors/")
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (Vect3 type-eq-decl nil vectors_3D_def "vectors/")
    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (zero const-decl "Vector" vectors_2D "vectors/")
    (/= const-decl "boolean" notequal nil)
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (nzv2 application-judgement "Nz_vect2" definitions_3D nil))
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    (bool nonempty-type-eq-decl nil booleans nil)
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    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (D formal-const-decl "posreal" vs_only nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (sq_nz_pos application-judgement "posreal" sq "reals/")
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
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   ((nzv2 application-judgement "Nz_vect2" definitions_3D nil)
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    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (Vect3 type-eq-decl nil vectors_3D_def "vectors/")
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    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (D formal-const-decl "posreal" vs_only nil)
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    (real_ge_is_total_order name-judgement "(total_order?[real])"
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    (sq_nz_pos application-judgement "posreal" sq "reals/")
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     "(strict_total_order?[real])" real_props nil)
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  (vs_exit_meets_circle_criterion_TCC2-1 nil 3471099186
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 (vs_exit_meets_circle_criterion 0
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    (nonneg_real nonempty-type-eq-decl nil real_types nil)
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    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
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    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (sq_nz_pos application-judgement "posreal" sq "reals/")
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_gt_is_strict_total_order name-judgement
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    (real_times_real_is_real application-judgement "real" reals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (Theta_D_exit_gt_0 formula-decl nil horizontal nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (Delta const-decl "real" horizontal nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nzint nonempty-type-eq-decl nil integers nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (Sign type-eq-decl nil sign "reals/")
    (Theta_D const-decl "real" horizontal nil)
    (vs_at_H formula-decl nil vertical nil)
    (H formal-const-decl "posreal" vs_only nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (* const-decl "Vector" vectors_3D "vectors/")
    (+ const-decl "Vector" vectors_3D "vectors/")
    (Vector type-eq-decl nil vectors_3D "vectors/")
    (real_plus_real_is_real application-judgement "real" reals nil)
    (vect2_add formula-decl nil vect_3D_2D "vectors/")
    (Theta_D_on_D formula-decl nil horizontal nil)
    (minus_nzreal_is_nzreal application-judgement "nzreal" real_types
     nil)
    (nonzero_abs_is_pos application-judgement "{y: posreal | y >= x}"
     real_defs nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (TRUE const-decl "bool" booleans nil)
    (id const-decl "(bijective?[T, T])" identity nil)
    (bijective? const-decl "bool" functions nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (both_sides_times_pos_ge1 formula-decl nil real_props nil)
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (nnreal_div_posreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (nzint_times_nzint_is_nzint application-judgement "nzint" integers
     nil)
    (zero_div formula-decl nil extra_tegies nil)
    (div_mult_pos_ge1 formula-decl nil real_props nil)
    (vs_at const-decl "real" vertical nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (not_horizontal_conflict_exit formula-decl nil horizontal nil)
    (* const-decl "Vector" vectors_2D "vectors/")
    (+ const-decl "Vector" vectors_2D "vectors/")
    (Delta_eq formula-decl nil horizontal nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (vect2_scal formula-decl nil vect_3D_2D "vectors/")
    (nzreal_times_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (nzreal nonempty-type-eq-decl nil reals nil)
    (circle_criterion? const-decl "bool" circle_criterion nil)
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (/= const-decl "boolean" notequal nil)
    (zero const-decl "Vector" vectors_2D "vectors/")
    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (Vect3 type-eq-decl nil vectors_3D_def "vectors/")
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (vect2 const-decl "Vect2" vect_3D_2D "vectors/")
    (Nzv2_vect3 type-eq-decl nil definitions_3D nil)
    (nzv2 application-judgement "Nz_vect2" definitions_3D nil))
   nil)))


¤ Dauer der Verarbeitung: 0.209 Sekunden  (vorverarbeitet)  ¤





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