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Datei: closest_approach_3D.prf   Sprache: Lisp

Untersuchung PVS©

(closest_approach_3D
 (sq_dist_lem 0
  (sq_dist_lem-1 nil 3256049050
   ("" (skosimp*)
    (("" (assert)
      (("" (rewrite "sq_dist_is_dist_sq")
        (("" (rewrite "dist_norm")
          (("" (expand "norm")
            (("" (rewrite "sq_sqrt")
              (("" (expand "sqv")
                (("" (expand "*")
                  (("" (expand "+")
                    (("" (expand "-") (("" (assertnil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((dist_norm formula-decl nil distance_3D nil)
    (sq_sqrt formula-decl nil sqrt "reals/")
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nnreal type-eq-decl nil real_types nil)
    (sqv const-decl "nnreal" vectors_3D nil)
    (- const-decl "Vector" vectors_3D nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (* const-decl "real" vectors_3D nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (norm const-decl "nnreal" vectors_3D nil)
    (* const-decl "Vector" vectors_3D 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)
    (+ const-decl "Vector" vectors_3D nil)
    (Vector type-eq-decl nil vectors_3D nil)
    (Vect3 type-eq-decl nil vectors_3D_def nil)
    (real nonempty-type-from-decl nil reals nil)
    (sq_dist_is_dist_sq formula-decl nil distance_3D nil))
   nil))
 (sq_dist_quad 0
  (sq_dist_quad-1 nil 3255774848
   ("" (skosimp*) (("" (grind) nil nil)) nil)
   ((real_minus_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (sq_dist const-decl "nnreal" distance_3D nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (+ const-decl "Vector" vectors_3D nil)
    (* const-decl "Vector" vectors_3D nil)
    (* const-decl "real" vectors_3D nil)
    (- const-decl "Vector" vectors_3D nil))
   shostak))
 (dist_eq_vel 0
  (dist_eq_vel-1 nil 3255968102 ("" (grind) nil nil)
   ((* const-decl "Vector" vectors_3D nil)
    (+ const-decl "Vector" vectors_3D nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (sq_dist const-decl "nnreal" distance_3D nil)
    (dist const-decl "nnreal" distance_3D nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil))
   shostak))
 (norm_diff_eq_0 0
  (norm_diff_eq_0-1 nil 3255967833
   ("" (skosimp*)
    (("" (rewrite "norm_eq_0")
      (("" (rewrite "sub_eq_zero")
        (("" (replaces -1)
          (("" (rewrite "dist_eq_vel")
            (("" (rewrite "dist_eq_vel"nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((norm_eq_0 formula-decl nil vectors_3D nil)
    (real nonempty-type-from-decl nil reals nil)
    (Vector type-eq-decl nil vectors_3D nil)
    (- const-decl "Vector" vectors_3D nil)
    (Vect3 type-eq-decl nil vectors_3D_def 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)
    (dist_eq_vel formula-decl nil closest_approach_3D nil)
    (sub_eq_zero formula-decl nil vectors_3D nil))
   shostak))
 (time_closest_TCC1 0
  (time_closest_TCC1-1 nil 3255962785
   ("" (skosimp*)
    (("" (rewrite "sq_eq_0")
      (("" (rewrite "norm_eq_0")
        (("" (assert) (("" (postpone) nil nil)) nil)) nil))
      nil))
    nil)
   ((sq_eq_0 formula-decl nil sq "reals/")
    (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)
    (Vector type-eq-decl nil vectors_3D nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nnreal type-eq-decl nil real_types nil)
    (norm const-decl "nnreal" vectors_3D nil)
    (- const-decl "Vector" vectors_3D nil)
    (Vect3 type-eq-decl nil vectors_3D_def nil))
   shostak))
 (time_closest_lem_TCC1 0
  (time_closest_lem_TCC1-1 nil 3256051573
   ("" (skosimp*)
    (("" (rewrite "dot_sq_norm")
      (("" (assert)
        (("" (replace -2)
          (("" (hide -2)
            (("" (hide -1)
              (("" (lemma "sq_eq_0")
                (("" (inst?) (("" (assertnil nil)) nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((dot_sq_norm formula-decl nil vectors_3D nil)
    (real nonempty-type-from-decl nil reals nil)
    (Vector type-eq-decl nil vectors_3D nil)
    (- const-decl "Vector" vectors_3D nil)
    (Vect3 type-eq-decl nil vectors_3D_def 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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nnreal type-eq-decl nil real_types nil)
    (norm const-decl "nnreal" vectors_3D nil)
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (sq_eq_0 formula-decl nil sq "reals/")
    (dot_scal_left formula-decl nil vectors_3D nil)
    (real_times_real_is_real application-judgement "real" reals nil))
   shostak))
 (time_closest_lem 0
  (time_closest_lem-1 nil 3256049208
   ("" (skosimp*)
    (("" (expand "time_closest")
      (("" (assert)
        (("" (rewrite "dot_sq_norm") (("" (assertnil nil)) nil))
        nil))
      nil))
    nil)
   ((time_closest const-decl "real" closest_approach_3D nil)
    (dot_sq_norm formula-decl nil vectors_3D nil)
    (real nonempty-type-from-decl nil reals nil)
    (Vector type-eq-decl nil vectors_3D nil)
    (- const-decl "Vector" vectors_3D nil)
    (Vect3 type-eq-decl nil vectors_3D_def nil)
    (dot_scal_left formula-decl nil vectors_3D nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (minus_real_is_real application-judgement "real" reals nil))
   shostak))
 (cpa_prep_mono 0
  (cpa_prep_mono-2 nil 3431333345
   ("" (skosimp*)
    (("" (expand "time_closest")
      (("" (assert)
        (("" (case "a!1 > 0")
          (("1" (lemma "quad_min_mono_inc")
            (("1" (inst - "a!1" "b!1" "c!1" "t2!1" "t1!1")
              (("1" (assert)
                (("1" (assert)
                  (("1" (prop)
                    (("1" (assert)
                      (("1" (rewrite "dot_sq_norm")
                        (("1" (lemma "sq_dist_quad")
                          (("1"
                            (inst -1 "a!1" "b!1" "c!1" "p0!1" "q0!1"
                             "t1!1" "u!1" "v!1" "w0!1")
                            (("1" (assert)
                              (("1"
                                (lemma "sq_dist_quad")
                                (("1"
                                  (inst
                                   -1
                                   "a!1"
                                   "b!1"
                                   "c!1"
                                   "p0!1"
                                   "q0!1"
                                   "t2!1"
                                   "u!1"
                                   "v!1"
                                   "w0!1")
                                  (("1"
                                    (assert)
                                    (("1"
                                      (expand "quadratic")
                                      (("1" (assertnil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (lemma "dot_sq_norm")
                      (("2" (inst?) (("2" (assertnil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (assertnil nil))
              nil))
            nil)
           ("2" (assert)
            (("2" (rewrite "dot_sq_norm")
              (("2" (lemma "sq_eq_0")
                (("2" (inst?) (("2" (assertnil nil)) nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((time_closest const-decl "real" closest_approach_3D 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)
    (/= const-decl "boolean" notequal nil)
    (a!1 skolem-const-decl "real" closest_approach_3D nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (sq_dist_quad formula-decl nil closest_approach_3D nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (quadratic const-decl "real" quadratic "reals/")
    (dot_sq_norm formula-decl nil vectors_3D nil)
    (Vector type-eq-decl nil vectors_3D nil)
    (- const-decl "Vector" vectors_3D nil)
    (Vect3 type-eq-decl nil vectors_3D_def 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)
    (quad_min_mono_inc formula-decl nil quad_minmax "reals/")
    (norm const-decl "nnreal" vectors_3D nil)
    (nnreal type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (sq_eq_0 formula-decl nil sq "reals/")
    (dot_scal_left formula-decl nil vectors_3D nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (minus_real_is_real application-judgement "real" reals nil))
   nil)
  (cpa_prep_mono-1 nil 3401722700
   ("" (skosimp*)
    (("" (expand "time_closest")
      (("" (assert)
        (("" (case "a!1 > 0")
          (("1" (lemma "quadratic_min_mono_inc")
            (("1"
              (inst - "a!1" "b!1" "c!1"
               "(LAMBDA t: sq_dist(p0!1 + t * u!1, q0!1 + t * v!1))"
               "t_cpa!1" "t2!1" "t1!1")
              (("1" (assert)
                (("1" (prop)
                  (("1" (apply-extensionality 1 :hide? t)
                    (("1" (lemma "sq_dist_quad")
                      (("1"
                        (inst -1 "a!1" "b!1" "c!1" "p0!1" "q0!1" "x!1"
                         "u!1" "v!1" "w0!1")
                        (("1" (assert)
                          (("1" (expand "quadratic")
                            (("1" (propax) nil nil)) nil))
                          nil))
                        nil))
                      nil)
                     ("2" (skosimp*)
                      (("2" (expand "quadratic")
                        (("2" (lemma "sq_dist_quad")
                          (("2"
                            (inst -1 "a!1" "b!1" "c!1" "p0!1" "q0!1"
                             "x1!1" "u!1" "v!1" "w0!1")
                            (("2" (assert) (("2" (assertnil nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (lemma "time_closest_lem")
                    (("2"
                      (inst -1 "a!1" "b!1" "p0!1" "q0!1" "u!1" "v!1")
                      (("2" (assert)
                        (("2" (expand "time_closest")
                          (("2" (assertnil nil)) nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (assertnil nil))
              nil))
            nil)
           ("2" (assert)
            (("2" (rewrite "dot_sq_norm")
              (("2" (lemma "sq_eq_0")
                (("2" (inst?) (("2" (assertnil nil)) nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((Vector type-eq-decl nil vectors_3D nil)
    (+ const-decl "Vector" vectors_3D nil)
    (Vect3 type-eq-decl nil vectors_3D_def nil)
    (* const-decl "Vector" vectors_3D nil)
    (quadratic const-decl "real" quadratic "reals/")
    (dot_sq_norm formula-decl nil vectors_3D nil)
    (norm const-decl "nnreal" vectors_3D nil)
    (sq_eq_0 formula-decl nil sq "reals/")
    (dot_scal_left formula-decl nil vectors_3D nil))
   nil))
 (time_cpa 0
  (time_cpa-3 nil 3431334821
   ("" (skosimp*)
    (("" (case "norm(u!1 - v!1) = 0")
      (("1" (expand "is_minimum?")
        (("1" (skosimp*)
          (("1" (lemma "norm_diff_eq_0")
            (("1" (inst -1 "p0!1" "q0!1" "t_cpa!1" "y!1" "u!1" "v!1")
              (("1" (assert)
                (("1" (assert)
                  (("1" (expand "dist")
                    (("1" (rewrite "sqrt_eq"nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (expand "time_closest")
        (("2" (name "A" "(u!1-v!1)*(u!1-v!1)")
          (("2" (name "B" "2*(p0!1-q0!1)*(u!1-v!1)")
            (("2" (name "C" "(p0!1-q0!1)*(p0!1-q0!1)")
              (("2" (case "A > 0")
                (("1" (assert)
                  (("1" (lemma "quad_min")
                    (("1" (inst -1 "A" "B" "C")
                      (("1" (assert)
                        (("1"
                          (case-replace
                           "(LAMBDA t: sq_dist(p0!1 + t * u!1, q0!1 + t * v!1)) = quadratic(A, B, C)")
                          (("1" (assert)
                            (("1" (lemma "dot_sq_norm")
                              (("1"
                                (inst - "(u!1 - v!1)")
                                (("1" (assertnil nil))
                                nil))
                              nil))
                            nil)
                           ("2" (apply-extensionality 1 :hide? t)
                            (("1" (lemma "sq_dist_quad")
                              (("1"
                                (inst
                                 -1
                                 "A"
                                 "B"
                                 "C"
                                 "p0!1"
                                 "q0!1"
                                 "x!1"
                                 "u!1"
                                 "v!1"
                                 "p0!1-q0!1")
                                (("1"
                                  (assert)
                                  (("1"
                                    (expand "quadratic")
                                    (("1" (propax) nil nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (skosimp*)
                              (("2"
                                (expand "quadratic")
                                (("2"
                                  (lemma "sq_dist_quad")
                                  (("2"
                                    (inst
                                     -1
                                     "A"
                                     "B"
                                     "C"
                                     "p0!1"
                                     "q0!1"
                                     "x1!1"
                                     "u!1"
                                     "v!1"
                                     "p0!1-q0!1")
                                    (("2"
                                      (assert)
                                      (("2" (assertnil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (lemma "dot_sq_norm")
                  (("2" (inst - "u!1-v!1")
                    (("2" (lemma "sq_eq_0")
                      (("2" (inst?) (("2" (assertnil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((Vect3 type-eq-decl nil vectors_3D_def nil)
    (- const-decl "Vector" vectors_3D nil)
    (norm const-decl "nnreal" vectors_3D nil)
    (nnreal type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals 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)
    (Vector type-eq-decl nil vectors_3D nil)
    (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)
    (* const-decl "Vector" vectors_3D nil)
    (+ const-decl "Vector" vectors_3D nil)
    (sq_dist const-decl "nnreal" distance_3D nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (sqrt_eq formula-decl nil sqrt "reals/")
    (dist const-decl "nnreal" distance_3D nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (norm_diff_eq_0 formula-decl nil closest_approach_3D nil)
    (is_minimum? const-decl "bool" quad_minmax "reals/")
    (* const-decl "real" vectors_3D nil)
    (sq_eq_0 formula-decl nil sq "reals/")
    (minus_real_is_real application-judgement "real" reals nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (dot_scal_left formula-decl nil vectors_3D nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (/= const-decl "boolean" notequal nil)
    (quadratic const-decl "real" quadratic "reals/")
    (dot_sq_norm formula-decl nil vectors_3D nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (sq_dist_quad formula-decl nil closest_approach_3D nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (A skolem-const-decl "real" closest_approach_3D nil)
    (B skolem-const-decl "real" closest_approach_3D nil)
    (C skolem-const-decl "real" closest_approach_3D nil)
    (quad_min formula-decl nil quad_minmax "reals/")
    (> const-decl "bool" reals nil)
    (time_closest const-decl "real" closest_approach_3D nil))
   nil)
  (time_cpa-2 nil 3421667499
   ("" (skosimp*)
    (("" (case "norm(u!1 - v!1) = 0")
      (("1" (expand "is_minimum?")
        (("1" (skosimp*)
          (("1" (lemma "norm_diff_eq_0")
            (("1" (inst -1 "p0!1" "q0!1" "t_cpa!1" "y!1" "u!1" "v!1")
              (("1" (assert)
                (("1" (assert)
                  (("1" (expand "dist")
                    (("1" (rewrite "sqrt_eq"nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (expand "time_closest")
        (("2" (name "A" "(u!1-v!1)*(u!1-v!1)")
          (("2" (name "B" "2*(p0!1-q0!1)*(u!1-v!1)")
            (("2" (name "C" "(p0!1-q0!1)*(p0!1-q0!1)")
              (("2" (case "A > 0")
                (("1" (lemma "quadratic_min")
                  (("1"
                    (inst -1 "A" "B" "C"
                     "(LAMBDA t: sq_dist(p0!1 + t * u!1, q0!1 + t * v!1))"
                     "t_cpa!1")
                    (("1" (assert)
                      (("1" (prop)
                        (("1" (apply-extensionality 1 :hide? t)
                          (("1" (lemma "sq_dist_quad")
                            (("1"
                              (inst -1 "A" "B" "C" "p0!1" "q0!1" "x!1"
                               "u!1" "v!1" "p0!1-q0!1")
                              (("1"
                                (assert)
                                (("1"
                                  (expand "quadratic")
                                  (("1" (propax) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (skosimp*)
                            (("2" (expand "quadratic")
                              (("2"
                                (lemma "sq_dist_quad")
                                (("2"
                                  (inst
                                   -1
                                   "A"
                                   "B"
                                   "C"
                                   "p0!1"
                                   "q0!1"
                                   "x1!1"
                                   "u!1"
                                   "v!1"
                                   "p0!1-q0!1")
                                  (("2"
                                    (assert)
                                    (("2" (assertnil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (lemma "time_closest_lem")
                          (("2"
                            (inst -1 "A" "B" "p0!1" "q0!1" "u!1" "v!1")
                            (("2" (assert)
                              (("2"
                                (assert)
                                (("2"
                                  (expand "time_closest")
                                  (("2" (assertnil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (assertnil nil))
                    nil))
                  nil)
                 ("2" (lemma "dot_sq_norm")
                  (("2" (inst - "u!1-v!1")
                    (("2" (lemma "sq_eq_0")
                      (("2" (inst?) (("2" (assertnil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((Vect3 type-eq-decl nil vectors_3D_def nil)
    (norm const-decl "nnreal" vectors_3D nil)
    (Vector type-eq-decl nil vectors_3D nil)
    (* const-decl "Vector" vectors_3D nil)
    (+ const-decl "Vector" vectors_3D nil)
    (sqrt_eq formula-decl nil sqrt "reals/")
    (* const-decl "real" vectors_3D nil)
    (dot_sq_norm formula-decl nil vectors_3D nil)
    (sq_eq_0 formula-decl nil sq "reals/")
    (dot_scal_left formula-decl nil vectors_3D nil)
    (quadratic const-decl "real" quadratic "reals/"))
   nil)
  (time_cpa-1 nil 3255788628
   ("" (skosimp*)
    (("" (lemma "cpa_prep")
      (("" (inst?)
        (("" (name "W0" "p0!1-q0!1")
          ((""
            (inst - "(u!1 - v!1) * (u!1 - v!1)" "2 * W0 * (u!1 - v!1)"
             " W0 * W0" "W0")
            (("" (assertnil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((Vector type-eq-decl nil vectors_3D nil)
    (* const-decl "Vector" vectors_3D nil)
    (* const-decl "real" vectors_3D nil))
   shostak))
 (dist_cpa 0
  (dist_cpa-1 nil 3255788937
   ("" (skosimp*)
    (("" (lemma "time_cpa")
      (("" (inst?)
        (("" (inst?)
          (("" (expand "is_minimum?")
            (("" (inst -1 "t!1")
              (("" (expand "dist") (("" (rewrite "sqrt_le"nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((time_cpa formula-decl nil closest_approach_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)
    (time_closest const-decl "real" closest_approach_3D nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (sqrt_le formula-decl nil sqrt "reals/")
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (nnreal type-eq-decl nil real_types nil)
    (sq_dist const-decl "nnreal" distance_3D nil)
    (Vector type-eq-decl nil vectors_3D nil)
    (+ const-decl "Vector" vectors_3D nil)
    (* const-decl "Vector" vectors_3D nil)
    (dist const-decl "nnreal" distance_3D nil)
    (is_minimum? const-decl "bool" quad_minmax "reals/")
    (Vect3 type-eq-decl nil vectors_3D_def nil)
    (real nonempty-type-from-decl nil reals nil))
   shostak))
 (dist_cpa_lt 0
  (dist_cpa_lt-1 nil 3401722756
   ("" (skosimp*)
    (("" (assert)
      (("" (lemma "cpa_prep_mono")
        (("" (inst?)
          (("" (name "W0" "p0!1-q0!1")
            ((""
              (inst - "(u!1 - v!1) * (u!1 - v!1)"
               "2 * W0 * (u!1 - v!1)" " W0 * W0" "t1!1" "t2!1" "W0")
              (("" (assertnil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real nonempty-type-from-decl nil reals nil)
    (Vect3 type-eq-decl nil vectors_3D_def 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)
    (* const-decl "Vector" vectors_3D nil)
    (* const-decl "real" vectors_3D nil)
    (- const-decl "Vector" vectors_3D nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (Vector type-eq-decl nil vectors_3D nil)
    (cpa_prep_mono formula-decl nil closest_approach_3D nil))
   nil))
 (dist_min 0
  (dist_min-1 nil 3255958397
   ("" (skosimp*)
    (("" (assert)
      (("" (flatten)
        (("" (lemma "dist_cpa")
          (("" (inst -1 "p0!1" "q0!1" "t1!1" "u!1" "v!1")
            (("" (assertnil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (dist_cpa formula-decl nil closest_approach_3D 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)
    (Vect3 type-eq-decl nil vectors_3D_def nil)
    (real nonempty-type-from-decl nil reals nil))
   shostak))
 (dist_diverges 0
  (dist_diverges-3 nil 3401722795
   ("" (skosimp*)
    (("" (assert)
      (("" (flatten)
        (("" (lemma "dist_cpa_lt")
          (("" (inst?)
            (("" (inst - "t1!1" "t2!1")
              (("" (assert)
                (("" (expand "dist")
                  (("" (lemma "sqrt_lt")
                    (("" (inst?) (("" (assertnil nil)) nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (dist_cpa_lt formula-decl nil closest_approach_3D nil)
    (dist const-decl "nnreal" distance_3D nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (nnreal type-eq-decl nil real_types nil)
    (sq_dist const-decl "nnreal" distance_3D nil)
    (Vector type-eq-decl nil vectors_3D nil)
    (+ const-decl "Vector" vectors_3D nil)
    (* const-decl "Vector" vectors_3D nil)
    (sqrt_lt formula-decl nil sqrt "reals/")
    (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)
    (Vect3 type-eq-decl nil vectors_3D_def nil)
    (real nonempty-type-from-decl nil reals nil))
   nil)
  (dist_diverges-2 nil 3401544437
   ("" (skosimp*)
    (("" (assert)
      (("" (flatten)
        (("" (case "t1!1 = time_closest(p0!1, q0!1, u!1, v!1)")
          (("1" (lemma "dist_min")
            (("1" (inst?)
              (("1" (assert)
                (("1" (assert) (("1" (inst?) nil nil)) nil)) nil))
              nil))
            nil)
           ("2" (case "norm(u!1-v!1)=0")
            (("1" (lemma "norm_diff_eq_0")
              (("1" (inst -1 "p0!1" "q0!1" "t1!1" "t2!1" "u!1" "v!1")
                (("1" (assertnil nil)) nil))
              nil)
             ("2" (rewrite "sq_dist_le")
              (("2" (hide 4)
                (("2" (name "A" "(u!1 - v!1) * (u!1 - v!1)")
                  (("2" (name "W0" "p0!1 - q0!1")
                    (("2" (name "B" "2 * W0 * (u!1 - v!1) ")
                      (("2" (name "C" "W0*W0")
                        (("2" (lemma "sq_dist_quad")
                          (("2" (inst?)
                            (("2" (inst -1 "A" "B" "C" "W0")
                              (("2"
                                (assert)
                                (("2"
                                  (replace -1)
                                  (("2"
                                    (hide -1)
                                    (("2"
                                      (lemma "sq_dist_quad")
                                      (("2"
                                        (inst?)
                                        (("2"
                                          (inst -1 "A" "B" "C" "W0")
                                          (("2"
                                            (assert)
                                            (("2"
                                              (replace -1)
                                              (("2"
                                                (hide -1)
                                                (("2"
                                                  (lemma
                                                   "sq_dist_quad")
                                                  (("2"
                                                    (inst?)
                                                    (("2"
                                                      (assert)
                                                      (("2"
                                                        (hide -1)
                                                        (("2"
                                                          (case-replace
                                                           "A > 0")
                                                          (("1"
                                                            (lemma
                                                             "quadratic_min_mono_inc")
                                                            (("1"
                                                              (inst
                                                               -1
                                                               "A"
                                                               "B"
                                                               "C"
                                                               "quadratic(A,B,C)"
                                                               "-B / (2 * A)"
                                                               "_"
                                                               "_")
                                                              (("1"
                                                                (inst
                                                                 -1
                                                                 "t2!1"
                                                                 "t1!1")
                                                                (("1"
                                                                  (assert)
                                                                  (("1"
                                                                    (expand
                                                                     "quadratic")
                                                                    (("1"
                                                                      (assert)
                                                                      (("1"
                                                                        (lemma
                                                                         "time_closest_lem")
                                                                        (("1"
                                                                          (inst?)
                                                                          (("1"
                                                                            (inst?)
                                                                            (("1"
                                                                              (assert)
                                                                              nil
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (assert)
                                                                nil
                                                                nil)
                                                               ("3"
                                                                (lemma
                                                                 "sq_eq_0")
                                                                (("3"
                                                                  (flatten)
                                                                  (("3"
                                                                    (assert)
                                                                    nil
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil)
                                                           ("2"
                                                            (rewrite
                                                             "dot_sq_norm"
                                                             -4)
                                                            (("2"
                                                              (assert)
                                                              (("2"
                                                                (lemma
                                                                 "sq_eq_0")
                                                                (("2"
                                                                  (inst?)
                                                                  (("2"
                                                                    (assert)
                                                                    nil
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((norm const-decl "nnreal" vectors_3D nil)
    (Vector type-eq-decl nil vectors_3D nil)
    (dot_scal_left formula-decl nil vectors_3D nil)
    (dot_sq_norm formula-decl nil vectors_3D nil)
    (sq_eq_0 formula-decl nil sq "reals/")
    (quadratic const-decl "real" quadratic "reals/")
    (* const-decl "real" vectors_3D nil)
    (+ const-decl "Vector" vectors_3D nil)
    (* const-decl "Vector" vectors_3D nil))
   nil)
  (dist_diverges-1 nil 3256916765
   ("" (skosimp*)
    (("" (assert)
      (("" (flatten)
        (("" (case "t2!1 = time_closest(p0!1, q0!1, u!1, v!1)")
          (("1" (lemma "dist_min")
            (("1" (inst?)
              (("1" (assert)
                (("1" (assert) (("1" (inst?) nil nil)) nil)) nil))
              nil))
            nil)
           ("2" (case "norm(u!1-v!1)=0")
            (("1" (lemma "norm_diff_eq_0")
              (("1" (inst -1 "p0!1" "q0!1" "t2!1" "tt!1" "u!1" "v!1")
                (("1" (assertnil nil)) nil))
              nil)
             ("2" (rewrite "sq_dist_le")
              (("2" (hide 4)
                (("2" (name "A" "(u!1 - v!1) * (u!1 - v!1)")
                  (("2" (name "W0" "p0!1 - q0!1")
                    (("2" (name "B" "2 * W0 * (u!1 - v!1) ")
                      (("2" (name "C" "W0*W0")
                        (("2" (lemma "sq_dist_quad")
                          (("2" (inst?)
                            (("2" (inst -1 "A" "B" "C" "W0")
                              (("2"
                                (assert)
                                (("2"
                                  (replace -1)
                                  (("2"
                                    (hide -1)
                                    (("2"
                                      (lemma "sq_dist_quad")
                                      (("2"
                                        (inst?)
                                        (("2"
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                                          (("2"
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                                            (("2"
                                              (replace -1)
                                              (("2"
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                                                  (("2"
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                                                    (("2"
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                                                      (("2"
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                                                        (("2"
                                                          (case-replace
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                                                          (("1"
                                                            (lemma
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                                                            (("1"
                                                              (inst
                                                               -1
                                                               "A"
                                                               "B"
                                                               "C"
                                                               "quadratic(A,B,C)"
                                                               "-B / (2 * A)"
                                                               "_"
                                                               "_")
                                                              (("1"
                                                                (inst
                                                                 -1
                                                                 "tt!1"
                                                                 "t2!1")
                                                                (("1"
                                                                  (assert)
                                                                  (("1"
                                                                    (expand
                                                                     "quadratic")
                                                                    (("1"
                                                                      (assert)
                                                                      (("1"
                                                                        (lemma
                                                                         "time_closest_lem")
                                                                        (("1"
                                                                          (inst?)
                                                                          (("1"
                                                                            (inst?)
                                                                            (("1"
                                                                              (assert)
                                                                              nil
                                                                              nil))
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                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (assert)
                                                                nil
                                                                nil)
                                                               ("3"
                                                                (lemma
                                                                 "sq_eq_0")
                                                                (("3"
                                                                  (flatten)
                                                                  (("3"
                                                                    (assert)
                                                                    nil
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil)
                                                           ("2"
                                                            (rewrite
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                                                             -4)
                                                            (("2"
                                                              (assert)
                                                              (("2"
                                                                (lemma
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                                                                (("2"
                                                                  (inst?)
                                                                  (("2"
                                                                    (assert)
                                                                    nil
                                                                    nil))
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                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((norm const-decl "nnreal" vectors_3D nil)
    (Vector type-eq-decl nil vectors_3D nil)
    (dot_scal_left formula-decl nil vectors_3D nil)
    (dot_sq_norm formula-decl nil vectors_3D nil)
    (sq_eq_0 formula-decl nil sq "reals/")
    (quadratic const-decl "real" quadratic "reals/")
    (* const-decl "real" vectors_3D nil)
    (+ const-decl "Vector" vectors_3D nil)
    (* const-decl "Vector" vectors_3D nil))
   nil))
 (dist_parallel_lines 0
  (dist_parallel_lines-1 nil 3401722823
   ("" (skosimp*)
    (("" (assert)
      (("" (flatten)
        (("" (expand "dist")
          (("" (lemma "sqrt_eq")
            (("" (inst?)
              (("" (flatten)
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                  (("" (split -1)
                    (("1" (propax) nil nil)
                     ("2" (hide 2)
                      (("2" (lemma "sq_dist_quad")
                        (("2" (name "W0" "p0!1-q0!1")
                          (("2" (inst?)
                            (("2"
                              (inst - "(u!1 - v!1) * (u!1 - v!1)"
                               "2 * W0 * (u!1 - v!1)" " W0 * W0" "W0")
                              (("2"
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                                (("2"
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                                  (("2"
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                                    (("2"
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                                      (("2"
                                        (inst?)
                                        (("2"
                                          (inst
                                           -
                                           "(u!1 - v!1) * (u!1 - v!1)"
                                           "2 * W0 * (u!1 - v!1)"
                                           " W0 * W0"
                                           "W0")
                                          (("2"
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                                              (("2"
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                                                (("1" (assertnil nil)
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                                                  (lemma "norm_eq_0")
                                                  (("2"
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                                                    (("2"
                                                      (assert)
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                    nil))
                  nil))
                nil))
              nil))
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          nil))
        nil))
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    nil)
   ((dist const-decl "nnreal" distance_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)
    (Vect3 type-eq-decl nil vectors_3D_def nil)
    (nnreal type-eq-decl nil real_types nil)
    (sq_dist const-decl "nnreal" distance_3D nil)
    (Vector type-eq-decl nil vectors_3D nil)
    (+ const-decl "Vector" vectors_3D nil)
    (* const-decl "Vector" vectors_3D nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (- const-decl "Vector" vectors_3D nil)
    (* const-decl "real" vectors_3D nil)
    (norm_eq_0 formula-decl nil vectors_3D nil)
    (dot_zero_right formula-decl nil vectors_3D nil)
    (zero const-decl "Vector" vectors_3D nil)
    (dot_scal_left formula-decl nil vectors_3D nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (sq_dist_quad formula-decl nil closest_approach_3D nil)
    (sqrt_eq formula-decl nil sqrt "reals/"))
   nil))
 (dot_nneg_tca_npos 0
  (dot_nneg_tca_npos-1 nil 3406994109
   ("" (skosimp)
    (("" (expand "time_closest")
      (("" (lift-if)
        (("" (prop)
          (("1" (rewrite "norm_eq_0")
            (("1" (replaces -1) (("1" (assertnil nil)) nil)) nil)
           ("2" (mult-by 2 " sq(norm(u!1 - v!1))")
            (("1" (assertnil nil) ("2" (rewrite "sq_gt_0"nil nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((time_closest const-decl "real" closest_approach_3D nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (Vect3 type-eq-decl nil vectors_3D_def nil)
    (- const-decl "Vector" vectors_3D nil)
    (Vector type-eq-decl nil vectors_3D nil)
    (real nonempty-type-from-decl nil reals nil)
    (norm_eq_0 formula-decl nil vectors_3D nil)
    (sq_gt_0 formula-decl nil sq "reals/")
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (div_cancel2 formula-decl nil real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (v!1 skolem-const-decl "Vect3" closest_approach_3D nil)
    (u!1 skolem-const-decl "Vect3" closest_approach_3D nil)
    (norm const-decl "nnreal" vectors_3D nil)
    (nnreal type-eq-decl nil real_types nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil) (> const-decl "bool" reals 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)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (* const-decl "real" vectors_3D nil)
    (both_sides_times_pos_le1 formula-decl nil real_props nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil))
   nil))
 (divergent_u_neq_v 0
  (divergent_u_neq_v-1 nil 3409339432
   ("" (skosimp)
    (("" (replaces -2)
      (("" (expand "divergent?") (("" (grind) 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)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (+ const-decl "Vector" vectors_3D nil)
    (* const-decl "Vector" vectors_3D nil)
    (dist const-decl "nnreal" distance_3D nil)
    (sq_dist const-decl "nnreal" distance_3D nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (divergent? const-decl "bool" closest_approach_3D nil))
   nil))
 (dot_nneg_divergent 0
  (dot_nneg_divergent-1 nil 3406994137
   ("" (skosimp)
    (("" (lemma "dot_nneg_tca_npos")
      (("" (inst? -1)
        (("" (assert)
          (("" (lemma "dist_diverges")
            (("" (expand "divergent?")
              (("" (skosimp)
                (("" (inst? -1)
                  (("" (inst -1 "0" "t!1" _)
                    (("" (inst? -1)
                      (("" (assert)
                        (("" (split -1)
                          (("1" (propax) nil nil)
                           ("2" (flatten)
                            (("2" (rewrite "norm_eq_0")
                              (("2" (rewrite "sub_eq_zero"nil nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((dot_nneg_tca_npos formula-decl nil closest_approach_3D nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (divergent? const-decl "bool" closest_approach_3D nil)
    (time_closest const-decl "real" closest_approach_3D nil)
    (- const-decl "Vector" vectors_3D nil)
    (Vector type-eq-decl nil vectors_3D nil)
    (norm_eq_0 formula-decl nil vectors_3D nil)
    (sub_eq_zero formula-decl nil vectors_3D nil)
    (add_zero_right formula-decl nil vectors_3D nil)
    (scal_0 formula-decl nil vectors_3D nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props 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_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)
    (dist_diverges formula-decl nil closest_approach_3D nil)
    (Vect3 type-eq-decl nil vectors_3D_def nil)
    (real nonempty-type-from-decl nil reals nil))
   nil))
 (divergent_dot_nneg 0
  (divergent_dot_nneg-1 nil 3411903251
   ("" (skosimp)
    (("" (case "divergent?(p0!1-q0!1,zero,u!1-v!1,zero)")
      (("1" (hide -2)
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          (("1" (flatten)
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              (("1" (name-replace "w" "u!1-v!1")
                (("1" (expand "divergent?")
                  (("1" (name "myt" "-(s*w)/sqv(w)")
                    (("1" (case "myt > 0")
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                        (("1" (expand "dist")
                          (("1" (rewrite "sqrt_lt")
                            (("1" (expand "sq_dist")
                              (("1"
                                (expand"*" "+")
                                (("1"
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                                             -3
                                             :dontdistrib
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                                            (("1"
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                     ("2" (flatten)
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                      nil))
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            nil)
           ("2" (use "divergent_u_neq_v")
            (("2" (assert)
              (("2" (flatten) (("2" (rewrite "norm_eq_0"nil nil))
                nil))
              nil))
            nil))
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        nil)
--> --------------------

--> maximum size reached

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

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