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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: egramcoq.mli   Sprache: Lisp

Original von: PVS©

(space_3D
 (conflict_symm 0
  (conflict_symm-1 nil 3471198645
   ("" (skeep)
    ((""
      (case "FORALL (s,v) : conflict?(s,v) IMPLIES conflict?(-s,-v)")
      (("1" (split)
        (("1" (flatten)
          (("1" (inst -2 "-s" "-v") (("1" (assertnil nil)) nil)) nil)
         ("2" (inst? -1) nil nil))
        nil)
       ("2" (hide 2)
        (("2" (skolem 1 ("sp" "vp"))
          (("2" (flatten)
            (("2" (expand "conflict?")
              (("2" (skeep -1)
                (("2" (inst 1 "nnt")
                  (("2" (split 1)
                    (("1" (hide -2) (("1" (grind) nil nil)) nil)
                     ("2" (hide -1) (("2" (grind) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((- const-decl "Vector" vectors_3D "vectors/")
    (Vector type-eq-decl nil vectors_3D "vectors/")
    (conflict? const-decl "bool" space_3D nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (Vect3 type-eq-decl nil vectors_3D_def "vectors/")
    (real nonempty-type-from-decl nil reals nil)
    (neg_neg formula-decl nil vectors_3D "vectors/")
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (nnreal type-eq-decl nil real_types nil)
    (>= const-decl "bool" 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)
    (number nonempty-type-decl nil numbers nil)
    (sq_nz_pos application-judgement "posreal" sq "reals/")
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (sqv const-decl "nnreal" vectors_2D "vectors/")
    (* const-decl "real" vectors_2D "vectors/")
    (+ const-decl "Vector" vectors_2D "vectors/")
    (* const-decl "Vector" vectors_2D "vectors/")
    (vect2 const-decl "Vect2" vect_3D_2D "vectors/")
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (minus_real_is_real application-judgement "real" reals nil))
   shostak))
 (conflict_ever 0
  (conflict_ever-1 nil 3470158403
   ("" (skeep)
    (("" (expand"conflict?" "conflict_ever?")
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      nil))
    nil)
   ((conflict_ever? const-decl "bool" space_3D nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (conflict? const-decl "bool" 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)
    (nnreal type-eq-decl nil real_types nil)
    (real_lt_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)
    (sq_nz_pos application-judgement "posreal" sq "reals/"))
   nil))
 (conflict_ever_shift 0
  (conflict_ever_shift-1 nil 3470158447
   ("" (skeep)
    (("" (split)
      (("1" (flatten)
        (("1" (expand "conflict_ever?")
          (("1" (skolem -1 "tt")
            (("1" (inst 1 "tt-t")
              (("1" (flatten)
                (("1" (split)
                  (("1" (hide -2)
                    (("1" (expand"+" "*") (("1" (assertnil nil))
                      nil))
                    nil)
                   ("2" (hide -1)
                    (("2" (rewrite "vect2_add")
                      (("2" (rewrite "vect2_scal")
                        (("2"
                          (case-replace
                           "vect2(s) + tt * vect2(v) = vect2(s) + t * vect2(v) + (tt - t) * vect2(v)")
                          (("2" (hide-all-but 1)
                            (("2" (grind) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (flatten)
        (("2" (expand "conflict_ever?")
          (("2" (skolem -1 "tt")
            (("2" (inst 1 "tt+t")
              (("2" (flatten)
                (("2" (split)
                  (("1" (hide -2)
                    (("1" (expand"+" "*") (("1" (assertnil nil))
                      nil))
                    nil)
                   ("2" (hide -1)
                    (("2"
                      (case-replace
                       "vect2(s + t * v) + tt * vect2(v) = vect2(s) + (tt + t) * vect2(v)")
                      (("2" (hide-all-but 1)
                        (("2" (rewrite "vect2_add")
                          (("2" (rewrite "vect2_scal")
                            (("2" (grind) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (conflict_ever? const-decl "bool" space_3D nil)
    (real_minus_real_is_real application-judgement "real" reals 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)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (* const-decl "Vector" vectors_3D "vectors/")
    (+ const-decl "Vector" vectors_3D "vectors/")
    (real_lt_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)
    (Vector type-eq-decl nil vectors_3D "vectors/")
    (Vect3 type-eq-decl nil vectors_3D_def "vectors/")
    (vect2_add formula-decl nil vect_3D_2D "vectors/")
    (* const-decl "Vector" vectors_2D "vectors/")
    (vect2 const-decl "Vect2" vect_3D_2D "vectors/")
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (+ const-decl "Vector" vectors_2D "vectors/")
    (= const-decl "[T, T -> boolean]" equalities nil)
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (vect2_scal formula-decl nil vect_3D_2D "vectors/")
    (+ const-decl "[numfield, numfield -> numfield]" number_fields
       nil))
   nil))
 (conflict_sum_closed 0
  (conflict_sum_closed-2 nil 3467454344
   ("" (skeep)
    (("" (expand "conflict?")
      (("" (skosimp*)
        (("" (case "nnt!1 = 0 and nnt!2 = 0")
          (("1" (flatten)
            (("1" (inst + "0")
              (("1" (assert)
                (("1" (replace -1) (("1" (assertnil nil)) nil)) nil))
              nil))
            nil)
           ("2" (name "tt" "nnt!2/(nnt!1 + nnt!2)")
            (("1" (label "ttname" -1)
              (("1" (case "0<=tt AND tt<=1")
                (("1" (flatten)
                  (("1" (name "newt" "(nnt!1*nnt!2)/(nnt!1 + nnt!2)")
                    (("1" (label "newtname" -1)
                      (("1"
                        (case "tt*nnt!1 = newt AND (1-tt)*nnt!2 = newt")
                        (("1" (flatten)
                          (("1" (label "newttt" -1)
                            (("1" (label "newtomtt" -2)
                              (("1"
                                (inst + "newt")
                                (("1"
                                  (name
                                   "VV"
                                   "vect2(s) + nnt!1 * vect2(v)")
                                  (("1"
                                    (label "vvname" -1)
                                    (("1"
                                      (name
                                       "WW"
                                       "vect2(s) + nnt!2 * vect2(w)")
                                      (("1"
                                        (label "wwname" -1)
                                        (("1"
                                          (name
                                           "VVz"
                                           "s`z + nnt!1 * v`z")
                                          (("1"
                                            (label "vvzname" -1)
                                            (("1"
                                              (name
                                               "WWz"
                                               "s`z + nnt!2 * w`z")
                                              (("1"
                                                (label "wwzname" -1)
                                                (("1"
                                                  (name
                                                   "VVt"
                                                   "s+nnt!1*v")
                                                  (("1"
                                                    (label
                                                     "vvtname"
                                                     -1)
                                                    (("1"
                                                      (name
                                                       "WWt"
                                                       "s+nnt!2*w")
                                                      (("1"
                                                        (label
                                                         "wwtname"
                                                         -1)
                                                        (("1"
                                                          (replace
                                                           "wwzname")
                                                          (("1"
                                                            (replace
                                                             "vvzname")
                                                            (("1"
                                                              (replace
                                                               "wwname")
                                                              (("1"
                                                                (replace
                                                                 "vvname")
                                                                (("1"
                                                                  (lemma
                                                                   "horiz_dist_convex_scaf")
                                                                  (("1"
                                                                    (inst
                                                                     -
                                                                     "VVt"
                                                                     "WWt-VVt")
                                                                    (("1"
                                                                      (case
                                                                       "s`z + newt * (v + w)`z = tt*VVz + (1-tt)*WWz AND vect2(s) + newt * vect2(v + w) = tt*VV+(1-tt)*WW")
                                                                      (("1"
                                                                        (flatten)
                                                                        (("1"
                                                                          (label
                                                                           "zfin"
                                                                           -1)
                                                                          (("1"
                                                                            (label
                                                                             "vectfin"
                                                                             -2)
                                                                            (("1"
                                                                              (replace
                                                                               "zfin")
                                                                              (("1"
                                                                                (replace
                                                                                 "vectfin")
                                                                                (("1"
                                                                                  (case
                                                                                   "convex?(LAMBDA (t): abs(t)-H)")
                                                                                  (("1"
                                                                                    (assert)
                                                                                    (("1"
                                                                                      (lemma
                                                                                       "convex_wtd_av_lt")
                                                                                      (("1"
                                                                                        (inst-cp
                                                                                         -
                                                                                         "0"
                                                                                         "LAMBDA (t): abs(t) - H"
                                                                                         "VVz"
                                                                                         "WWz")
                                                                                        (("1"
                                                                                          (inst
                                                                                           -
                                                                                           "0"
                                                                                           "LAMBDA (t): horiz_dist_scaf(VVt)(t, WWt - VVt)"
                                                                                           "0"
                                                                                           "1")
                                                                                          (("1"
                                                                                            (assert)
                                                                                            (("1"
                                                                                              (expand
                                                                                               "horiz_dist_scaf"
                                                                                               -1
                                                                                               1)
                                                                                              (("1"
                                                                                                (expand
                                                                                                 "horiz_dist_scaf"
                                                                                                 -1
                                                                                                 1)
                                                                                                (("1"
                                                                                                  (assert)
                                                                                                  (("1"
                                                                                                    (case
                                                                                                     "vect2(VVt) = VV AND vect2(VVt)+vect2(WWt-VVt) = WW")
                                                                                                    (("1"
                                                                                                      (flatten)
                                                                                                      (("1"
                                                                                                        (assert)
                                                                                                        (("1"
                                                                                                          (inst
                                                                                                           -
                                                                                                           "tt")
                                                                                                          (("1"
                                                                                                            (inst
                                                                                                             -
                                                                                                             "tt")
                                                                                                            (("1"
                                                                                                              (assert)
                                                                                                              (("1"
                                                                                                                (expand
                                                                                                                 "horiz_dist_scaf")
                                                                                                                (("1"
                                                                                                                  (case-replace
                                                                                                                   "vect2(VVt) + (1 - tt) * vect2(WWt - VVt) = tt * VV + (1 - tt) * WW")
                                                                                                                  (("1"
                                                                                                                    (assert)
                                                                                                                    nil
                                                                                                                    nil)
                                                                                                                   ("2"
                                                                                                                    (hide-all-but
                                                                                                                     (-1
                                                                                                                      -2
                                                                                                                      1))
                                                                                                                    (("2"
                                                                                                                      (grind)
                                                                                                                      nil
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil)
                                                                                                     ("2"
                                                                                                      (hide-all-but
                                                                                                       ("vvtname"
                                                                                                        "vvname"
                                                                                                        "wwtname"
                                                                                                        "wwname"
                                                                                                        1))
                                                                                                      (("2"
                                                                                                        (replace
                                                                                                         "wwtname"
                                                                                                         +
                                                                                                         rl)
                                                                                                        (("2"
                                                                                                          (replace
                                                                                                           "vvtname"
                                                                                                           +
                                                                                                           rl)
                                                                                                          (("2"
                                                                                                            (replace
                                                                                                             "vvname"
                                                                                                             +
                                                                                                             rl)
                                                                                                            (("2"
                                                                                                              (replace
                                                                                                               "wwname"
                                                                                                               +
                                                                                                               rl)
                                                                                                              (("2"
                                                                                                                (rewrite
                                                                                                                 "vect2_add")
                                                                                                                (("2"
                                                                                                                  (rewrite
                                                                                                                   "vect2_sub")
                                                                                                                  (("2"
                                                                                                                    (rewrite
                                                                                                                     "vect2_add")
                                                                                                                    (("2"
                                                                                                                      (rewrite
                                                                                                                       "vect2_add")
                                                                                                                      (("2"
                                                                                                                        (rewrite
                                                                                                                         "vect2_scal")
                                                                                                                        (("2"
                                                                                                                          (rewrite
                                                                                                                           "vect2_scal")
                                                                                                                          (("2"
                                                                                                                            (hide-all-but
                                                                                                                             1)
                                                                                                                            (("2"
                                                                                                                              (grind)
                                                                                                                              nil
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil)
                                                                                   ("2"
                                                                                    (lemma
                                                                                     "abs_linear_convex")
                                                                                    (("2"
                                                                                      (inst
                                                                                       -
                                                                                       "H"
                                                                                       "0"
                                                                                       "1")
                                                                                      (("2"
                                                                                        (assert)
                                                                                        nil
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (replace
                                                                         "vvname"
                                                                         +
                                                                         rl)
                                                                        (("2"
                                                                          (replace
                                                                           "wwname"
                                                                           +
                                                                           rl)
                                                                          (("2"
                                                                            (replace
                                                                             "vvzname"
                                                                             +
                                                                             rl)
                                                                            (("2"
                                                                              (replace
                                                                               "wwzname"
                                                                               +
                                                                               rl)
                                                                              (("2"
                                                                                (assert)
                                                                                (("2"
                                                                                  (hide
                                                                                   (2
                                                                                    3
                                                                                    4
                                                                                    5))
                                                                                  (("2"
                                                                                    (split
                                                                                     1)
                                                                                    (("1"
                                                                                      (copy
                                                                                       "newtomtt")
                                                                                      (("1"
                                                                                        (mult-by
                                                                                         -1
                                                                                         "w`z")
                                                                                        (("1"
                                                                                          (assert)
                                                                                          (("1"
                                                                                            (replace
                                                                                             -1)
                                                                                            (("1"
                                                                                              (hide
                                                                                               -1)
                                                                                              (("1"
                                                                                                (replace
                                                                                                 "newttt"
                                                                                                 +
                                                                                                 rl)
                                                                                                (("1"
                                                                                                  (rewrite
                                                                                                   "vz_distr_add")
                                                                                                  (("1"
                                                                                                    (assert)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil)
                                                                                     ("2"
                                                                                      (hide-all-but
                                                                                       ("newttt"
                                                                                        "newtomtt"
                                                                                        1))
                                                                                      (("2"
                                                                                        (grind)
                                                                                        nil
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
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                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (lemma
                                   "nnreal_div_posreal_is_nnreal")
                                  (("2"
                                    (inst
                                     -
                                     "(nnt!1*nnt!2)"
                                     "nnt!1 + nnt!2")
                                    (("1"
                                      (hide-all-but (-1 "newtname" 1))
                                      (("1" (grind) nil nil))
                                      nil)
                                     ("2" (assertnil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (replace "newtname" + rl)
                          (("2" (replace "ttname" + rl)
                            (("2" (hide-all-but (1 2))
                              (("2"
                                (ground)
                                (("2" (field 2) nil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (lemma "nnreal_div_posreal_is_nnreal")
                  (("2" (inst - "nnt!2" "nnt!1 + nnt!2")
                    (("1" (replace "ttname" -)
                      (("1" (assert)
                        (("1" (replace "ttname" + rl)
                          (("1" (cross-mult 1) (("1" (assertnil nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (assertnil nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (assertnil nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (conflict? const-decl "bool" space_3D nil)
    (nnreal type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals 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)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (number nonempty-type-decl nil numbers nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (add_zero_right formula-decl nil vectors_2D "vectors/")
    (scal_0 formula-decl nil vectors_2D "vectors/")
    (real_lt_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)
    (sq_nz_pos application-judgement "posreal" sq "reals/")
    (div_mult_pos_le1 formula-decl nil real_props nil)
    (TRUE const-decl "bool" booleans nil)
    (id const-decl "(bijective?[T, T])" identity nil)
    (bijective? const-decl "bool" functions nil)
    (div_cancel2 formula-decl nil real_props nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (both_sides_times1 formula-decl nil real_props nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (nnreal_div_posreal_is_nnreal judgement-tcc nil real_types nil)
    (nnt!2 skolem-const-decl "nnreal" space_3D nil)
    (nnt!1 skolem-const-decl "nnreal" space_3D nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (+ const-decl "Vector" 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/")
    (* const-decl "Vector" vectors_2D "vectors/")
    (Vector type-eq-decl nil vectors_3D "vectors/")
    (+ const-decl "Vector" vectors_3D "vectors/")
    (* const-decl "Vector" vectors_3D "vectors/")
    (real_minus_real_is_real application-judgement "real" reals nil)
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (horiz_dist_convex_scaf formula-decl nil horizontal_dist_convexity
     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" space_3D nil)
    (convex? const-decl "bool" convex_functions "reals/")
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (H formal-const-decl "posreal" space_3D nil)
    (convex_wtd_av_lt formula-decl nil convex_functions "reals/")
    (horiz_dist_scaf const-decl "real" horizontal_dist_convexity nil)
    (scal_1 formula-decl nil vectors_2D "vectors/")
    (vect2_sub formula-decl nil vect_3D_2D "vectors/")
    (- const-decl "Vector" vectors_2D "vectors/")
    (vect2_scal formula-decl nil vect_3D_2D "vectors/")
    (vect2_add formula-decl nil vect_3D_2D "vectors/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (abs_linear_convex formula-decl nil convex_functions "reals/")
    (vz_distr_add formula-decl nil vectors_3D "vectors/")
    (both_sides_times1_imp formula-decl nil extra_real_props nil)
    (- const-decl "Vector" vectors_3D "vectors/")
    (newt skolem-const-decl "real" space_3D nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (<= const-decl "bool" reals 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)
    (/= const-decl "boolean" notequal nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil))
   nil)
  (conflict_sum_closed-1 nil 3467382877
   ("" (skeep)
    (("" (expand "conflict?")
      (("" (skolem -1 "ntt1")
        (("" (skolem -2 "ntt2")
          (("" (flatten)
            (("" (rewrite "vect2_add") (("" (postpone) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   nil shostak))
 (conflict_is_an_open_set 0
  (conflict_is_an_open_set-1 nil 3566319824
   ("" (skeep)
    (("" (expand "conflict?" -1)
      (("" (skosimp*)
        (("" (label "underH" -1)
          (("" (label "underD" -2)
            (("" (case "nnt!1 /= 0")
              (("1" (flatten)
                (("1" (name "del1" "H - abs(ss`z + nnt!1 * vv`z)")
                  (("1" (label "del1name" -1)
                    (("1"
                      (name "del2"
                            "D - norm(vect2(ss) + nnt!1 * vect2(vv))")
                      (("1" (label "del2name" -1)
                        (("1" (case "del2 > 0")
                          (("1" (label "del2pos" -1)
                            (("1" (hide "del2pos")
                              (("1"
                                (name "delta" "min(del1,del2)")
                                (("1"
                                  (label "deltaname" -1)
                                  (("1"
                                    (inst + "delta/(2*nnt!1)")
                                    (("1"
                                      (skeep 2)
                                      (("1"
                                        (case
                                         "norm(ww) >= abs(ww`z) AND norm(ww) >= norm(vect2(ww))")
                                        (("1"
                                          (label "normlem" -1)
                                          (("1"
                                            (hide "normlem")
                                            (("1"
                                              (expand "conflict?")
                                              (("1"
                                                (inst + "nnt!1")
                                                (("1"
                                                  (split 2)
                                                  (("1"
                                                    (lemma "triangle")
                                                    (("1"
                                                      (rewrite
                                                       "vz_distr_add")
                                                      (("1"
                                                        (assert)
                                                        (("1"
                                                          (inst
                                                           -
                                                           "ss`z + vv`z*nnt!1"
                                                           "ww`z*nnt!1")
                                                          (("1"
                                                            (case
                                                             "abs(ww`z*nnt!1) < del1")
                                                            (("1"
                                                              (assert)
                                                              nil
                                                              nil)
                                                             ("2"
                                                              (hide 2)
                                                              (("2"
                                                                (rewrite
                                                                 "abs_mult")
                                                                (("2"
                                                                  (case
                                                                   "abs(nnt!1) = nnt!1")
                                                                  (("1"
                                                                    (replace
                                                                     -1)
                                                                    (("1"
                                                                      (reveal
                                                                       "normlem")
                                                                      (("1"
                                                                        (flatten)
                                                                        (("1"
                                                                          (div-by
                                                                           1
                                                                           "nnt!1")
                                                                          (("1"
                                                                            (case
                                                                             "del1 / nnt!1 >= delta / (2 * nnt!1)")
                                                                            (("1"
                                                                              (assert)
                                                                              nil
                                                                              nil)
                                                                             ("2"
                                                                              (hide
                                                                               2)
                                                                              (("2"
                                                                                (cross-mult
                                                                                 1)
                                                                                (("2"
                                                                                  (div-by
                                                                                   1
                                                                                   "nnt!1")
                                                                                  (("2"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (expand
                                                                     "abs")
                                                                    (("2"
                                                                      (propax)
                                                                      nil
                                                                      nil))
                                                                    nil))
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                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil)
                                                   ("2"
                                                    (case
                                                     "norm(vect2(ss) + nnt!1 * vect2(vv + ww)) < D")
                                                    (("1"
                                                      (lemma "sq_lt")
                                                      (("1"
                                                        (inst?)
                                                        (("1"
                                                          (assert)
                                                          (("1"
                                                            (lemma
                                                             "vectors_2D.sqrt_sqv_norm")
                                                            (("1"
                                                              (inst?)
                                                              (("1"
                                                                (replace
                                                                 -1
                                                                 :dir
                                                                 rl)
                                                                (("1"
                                                                  (rewrite
                                                                   "vect2_add")
                                                                  (("1"
                                                                    (assert)
                                                                    nil
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil)
                                                     ("2"
                                                      (hide 2)
                                                      (("2"
                                                        (rewrite
                                                         "vect2_add")
                                                        (("2"
                                                          (lemma
                                                           "vectors_2D.norm_add_le")
                                                          (("2"
                                                            (inst
                                                             -
                                                             "vect2(ss) + nnt!1*vect2(vv)"
                                                             "nnt!1*vect2(ww)")
                                                            (("2"
                                                              (assert)
                                                              (("2"
                                                                (case
                                                                 "norm(nnt!1 * vect2(ww)) + norm(vect2(ss) + nnt!1 * vect2(vv)) < D")
                                                                (("1"
                                                                  (case
                                                                   "vect2(ss) + nnt!1 * vect2(vv) + nnt!1 * vect2(ww) = vect2(ss) + nnt!1 * (vect2(vv) + vect2(ww))")
                                                                  (("1"
                                                                    (assert)
                                                                    nil
                                                                    nil)
                                                                   ("2"
                                                                    (hide
                                                                     2)
                                                                    (("2"
                                                                      (hide-all-but
                                                                       1)
                                                                      (("2"
                                                                        (grind)
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                                                                    nil))
                                                                  nil)
                                                                 ("2"
                                                                  (case
                                                                   "norm(nnt!1*vect2(ww)) < del2")
                                                                  (("1"
                                                                    (assert)
                                                                    nil
                                                                    nil)
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                                                                    (hide
                                                                     2)
                                                                    (("2"
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                                                                       2)
                                                                      (("2"
                                                                        (rewrite
                                                                         "norm_scal")
                                                                        (("2"
                                                                          (case
                                                                           "abs(nnt!1) = nnt!1")
                                                                          (("1"
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                                                                             -1)
                                                                            (("1"
                                                                              (div-by
                                                                               1
                                                                               "nnt!1")
                                                                              (("1"
                                                                                (case
                                                                                 "del2 / nnt!1 >= delta/(2*nnt!1)")
                                                                                (("1"
                                                                                  (reveal
                                                                                   "normlem")
                                                                                  (("1"
                                                                                    (flatten)
                                                                                    (("1"
                                                                                      (assert)
                                                                                      nil
                                                                                      nil))
                                                                                    nil))
                                                                                  nil)
                                                                                 ("2"
                                                                                  (hide
                                                                                   2)
--> --------------------

--> maximum size reached

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

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