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Datei: opt_line.prf Sprache: Lisp

Original von: PVS^©

(opt_line
(opt_line_eps_TCC1 0
  (opt_line_eps_TCC1-1 nil 3441660997
   ("" (skeep) (("" (assert) nil nil)) nil)
   ((real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   nil))
(opt_line_eps_TCC2 0
  (opt_line_eps_TCC2-1 nil 3441660997 ("" (skosimp*) nil nil) nil nil))
(opt_line_eps_tangent_line 0
  (opt_line_eps_tangent_line-3 nil 3445708851
   ("" (skeep)
    (("" (expand "opt_line_eps?")
      (("" (flatten)
        (("" (expand "opt_line_eps" :assert? none)
          (("" (skoletin -1 :postfix "a")
            (("" (lift-if)
              (("" (split -)
                (("1" (flatten)
                  (("1"
                    (typepred
                     "opt_trk_gs_line(tangent_line(sp, eps),vo, vi)")
                    (("1" (replaces (-4 -5) :dir rl)
                      (("1" (expand "tangent_line?")
                        (("1" (inst?) (("1" (assert) nil nil)) nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (flatten) nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((opt_line_eps? const-decl "bool" opt_line nil)
    (opt_line_eps const-decl
     "{nvo: Vect2 | nvo /= zero => optimal?(vo, tangent_line(sp, eps))(nvo)}"
     opt_line nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ka skolem-const-decl "real" opt_line nil)
    (tangent_line? const-decl "bool" tangent_line nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (tangent_line const-decl "Nz_vect2" tangent_line 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)
    (Sp_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)
    (opt_trk_gs_line const-decl
     "{k: real, nvo: (optimal?(vo, nzv)) | k * nzv = nvo - vi}"
     opt_trk_gs nil)
    (D formal-const-decl "posreal" opt_line 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)
    (- const-decl "Vector" vectors_2D "vectors/")
    (* const-decl "Vector" vectors_2D "vectors/")
    (optimal? const-decl "bool" definitions nil)
    (bool nonempty-type-eq-decl nil booleans 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)
    (Vect2 type-eq-decl nil vectors_2D_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/")
    (real nonempty-type-from-decl nil reals nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (IFF const-decl "[bool, bool -> bool]" booleans nil))
   nil)
  (opt_line_eps_tangent_line-2 nil 3445706887
   ("" (skeep)
    (("" (beta)
      (("" (flatten)
        ((""
          (name-replace "opto" "opt_line_eps(sp, vo, vi, eps)" :hide?
           nil)
          (("" (expand "opt_line_eps" :assert? none)
            (("" (skoletin -1 :postfix "a")
              (("" (lift-if)
                (("" (split -)
                  (("1" (flatten)
                    (("1"
                      (typepred
                       "opt_trk_gs_line(tangent_line(sp, eps),vo, vi)")
                      (("1" (replaces (-4 -5) :dir rl)
                        (("1" (expand "tangent_line?")
                          (("1" (inst?) (("1" (assert) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (flatten) (("2" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (sqv const-decl "nnreal" vectors_2D "vectors/")
    (sq const-decl "nonneg_real" sq "reals/")
    (Sp_vect2 type-eq-decl nil horizontal nil)
    (Sign type-eq-decl nil sign "reals/")
    (zero const-decl "Vector" vectors_2D "vectors/")
    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (tangent_line const-decl "Nz_vect2" tangent_line nil)
    (opt_trk_gs_line const-decl
     "{k: real, nvo: (optimal?(vo, nzv)) | k * nzv = nvo - vi}"
     opt_trk_gs nil)
    (* const-decl "Vector" vectors_2D "vectors/")
    (tangent_line? const-decl "bool" tangent_line nil))
   nil)
  (opt_line_eps_tangent_line-1 nil 3433323791
   ("" (skeep)
    (("" (beta)
      (("" (flatten)
        ((""
          (name-replace "opto" "opt_line_eps(sp, vo, vi, eps)" :hide?
           nil)
          (("" (expand "opt_line_eps")
            (("" (assert) (("" (postpone) nil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((tangent_line const-decl "Nz_vect2" tangent_line nil)
    (Sign type-eq-decl nil sign "reals/")
    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (zero const-decl "Vector" vectors_2D "vectors/")
    (Sp_vect2 type-eq-decl nil horizontal nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (sqv const-decl "nnreal" vectors_2D "vectors/")
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (tangent_line? const-decl "bool" tangent_line nil)
    (* const-decl "Vector" vectors_2D "vectors/")
    (opt_trk_gs_line const-decl
     "{k: real, nvo: (optimal?(vo, nzv)) | k * nzv = nvo - vi}"
     opt_trk_gs nil))
   nil))
(opt_line_is_line_solution 0
  (opt_line_is_line_solution-1 nil 3471194384
   ("" (skeep)
    (("" (lemma "opt_line_eps_tangent_line")
      (("" (inst?)
        (("" (assert)
          (("" (lemma "tangent_line_solution")
            (("" (inst?) (("" (assert) nil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((opt_line_eps_tangent_line formula-decl nil opt_line nil)
    (- const-decl "Vector" vectors_2D "vectors/")
    (tangent_line_solution formula-decl nil tangent_line nil)
    (Sp_vect2 type-eq-decl nil horizontal nil)
    (D formal-const-decl "posreal" opt_line nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (sqv const-decl "nnreal" vectors_2D "vectors/")
    (nnreal type-eq-decl nil real_types nil)
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (>= const-decl "bool" reals nil)
    (Vect2 type-eq-decl nil vectors_2D_def "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)
    (bool nonempty-type-eq-decl nil 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)
    (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))
   shostak)))

¤ Dauer der Verarbeitung: 0.19 Sekunden (vorverarbeitet) ¤

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