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Datei: digraph_inductions.pvs   Sprache: Lisp

Original von: PVS©

(closest_approach_2D
 (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_2D 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_2D nil)
    (- const-decl "Vector" vectors_2D nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (* const-decl "real" vectors_2D 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_2D nil)
    (* const-decl "Vector" vectors_2D 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_2D nil)
    (Vector type-eq-decl nil vectors_2D nil)
    (Vect2 type-eq-decl nil vectors_2D_def nil)
    (real nonempty-type-from-decl nil reals nil)
    (sq_dist_is_dist_sq formula-decl nil distance_2D 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_2D nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (+ const-decl "Vector" vectors_2D nil)
    (* const-decl "Vector" vectors_2D nil)
    (* const-decl "real" vectors_2D nil)
    (- const-decl "Vector" vectors_2D nil))
   shostak))
 (dist_eq_vel 0
  (dist_eq_vel-1 nil 3255968102 ("" (grind) nil nil)
   ((* const-decl "Vector" vectors_2D nil)
    (+ const-decl "Vector" vectors_2D nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (sq_dist const-decl "nnreal" distance_2D nil)
    (dist const-decl "nnreal" distance_2D 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_2D nil)
    (real nonempty-type-from-decl nil reals nil)
    (Vector type-eq-decl nil vectors_2D nil)
    (- const-decl "Vector" vectors_2D nil)
    (Vect2 type-eq-decl nil vectors_2D_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_2D nil)
    (sub_eq_zero formula-decl nil vectors_2D 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_2D 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_2D nil)
    (- const-decl "Vector" vectors_2D nil)
    (Vect2 type-eq-decl nil vectors_2D_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_2D nil)
    (real nonempty-type-from-decl nil reals nil)
    (Vector type-eq-decl nil vectors_2D nil)
    (- const-decl "Vector" vectors_2D nil)
    (Vect2 type-eq-decl nil vectors_2D_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_2D 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_2D 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_2D nil)
    (dot_sq_norm formula-decl nil vectors_2D nil)
    (real nonempty-type-from-decl nil reals nil)
    (Vector type-eq-decl nil vectors_2D nil)
    (- const-decl "Vector" vectors_2D nil)
    (Vect2 type-eq-decl nil vectors_2D_def nil)
    (dot_scal_left formula-decl nil vectors_2D 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-1 nil 3401721075
   ("" (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_2D 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_2D nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (sq_dist_quad formula-decl nil closest_approach_2D nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (quadratic const-decl "real" quadratic "reals/")
    (dot_sq_norm formula-decl nil vectors_2D nil)
    (Vector type-eq-decl nil vectors_2D nil)
    (- const-decl "Vector" vectors_2D nil)
    (Vect2 type-eq-decl nil vectors_2D_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_2D 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_2D 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))
 (time_cpa 0
  (time_cpa-2 nil 3421666755
   ("" (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)
   ((Vect2 type-eq-decl nil vectors_2D_def nil)
    (- const-decl "Vector" vectors_2D nil)
    (norm const-decl "nnreal" vectors_2D 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_2D 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_2D nil)
    (+ const-decl "Vector" vectors_2D nil)
    (sq_dist const-decl "nnreal" distance_2D nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (sqrt_eq formula-decl nil sqrt "reals/")
    (dist const-decl "nnreal" distance_2D nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (norm_diff_eq_0 formula-decl nil closest_approach_2D nil)
    (is_minimum? const-decl "bool" quad_minmax "reals/")
    (* const-decl "real" vectors_2D 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_2D 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_2D nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (sq_dist_quad formula-decl nil closest_approach_2D nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (A skolem-const-decl "real" closest_approach_2D nil)
    (B skolem-const-decl "real" closest_approach_2D nil)
    (C skolem-const-decl "real" closest_approach_2D nil)
    (quad_min formula-decl nil quad_minmax "reals/")
    (> const-decl "bool" reals nil)
    (time_closest const-decl "real" closest_approach_2D nil))
   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_2D nil)
    (* const-decl "Vector" vectors_2D nil)
    (* const-decl "real" vectors_2D 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_2D 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_2D 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_2D nil)
    (Vector type-eq-decl nil vectors_2D nil)
    (+ const-decl "Vector" vectors_2D nil)
    (* const-decl "Vector" vectors_2D nil)
    (dist const-decl "nnreal" distance_2D nil)
    (is_minimum? const-decl "bool" quad_minmax "reals/")
    (Vect2 type-eq-decl nil vectors_2D_def nil)
    (real nonempty-type-from-decl nil reals nil))
   shostak))
 (dist_cpa_lt 0
  (dist_cpa_lt-1 nil 3401721539
   ("" (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)
    (Vect2 type-eq-decl nil vectors_2D_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_2D nil)
    (* const-decl "real" vectors_2D nil)
    (- const-decl "Vector" vectors_2D nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (Vector type-eq-decl nil vectors_2D nil)
    (cpa_prep_mono formula-decl nil closest_approach_2D 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_2D 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)
    (Vect2 type-eq-decl nil vectors_2D_def nil)
    (real nonempty-type-from-decl nil reals nil))
   shostak))
 (dist_diverges 0
  (dist_diverges-3 nil 3401721639
   ("" (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_2D nil)
    (dist const-decl "nnreal" distance_2D 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_2D nil)
    (Vector type-eq-decl nil vectors_2D nil)
    (+ const-decl "Vector" vectors_2D nil)
    (* const-decl "Vector" vectors_2D 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)
    (Vect2 type-eq-decl nil vectors_2D_def nil)
    (real nonempty-type-from-decl nil reals nil))
   nil)
  (dist_diverges-2 nil 3401544302
   ("" (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_2D nil)
    (Vector type-eq-decl nil vectors_2D nil)
    (dot_scal_left formula-decl nil vectors_2D nil)
    (dot_sq_norm formula-decl nil vectors_2D nil)
    (sq_eq_0 formula-decl nil sq "reals/")
    (quadratic const-decl "real" quadratic "reals/")
    (* const-decl "real" vectors_2D nil)
    (+ const-decl "Vector" vectors_2D nil)
    (* const-decl "Vector" vectors_2D 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"
                                          (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
                                                                 "tt!1"
                                                                 "t2!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_2D nil)
    (Vector type-eq-decl nil vectors_2D nil)
    (dot_scal_left formula-decl nil vectors_2D nil)
    (dot_sq_norm formula-decl nil vectors_2D nil)
    (sq_eq_0 formula-decl nil sq "reals/")
    (quadratic const-decl "real" quadratic "reals/")
    (* const-decl "real" vectors_2D nil)
    (+ const-decl "Vector" vectors_2D nil)
    (* const-decl "Vector" vectors_2D nil))
   nil))
 (dist_parallel_lines 0
  (dist_parallel_lines-1 nil 3401721568
   ("" (skosimp*)
    (("" (assert)
      (("" (flatten)
        (("" (expand "dist")
          (("" (lemma "sqrt_eq")
            (("" (inst?)
              (("" (flatten)
                (("" (hide -1)
                  (("" (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"
                                (assert)
                                (("2"
                                  (replace -2)
                                  (("2"
                                    (hide -2)
                                    (("2"
                                      (lemma "sq_dist_quad")
                                      (("2"
                                        (inst?)
                                        (("2"
                                          (inst
                                           -
                                           "(u!1 - v!1) * (u!1 - v!1)"
                                           "2 * W0 * (u!1 - v!1)"
                                           " W0 * W0"
                                           "W0")
                                          (("2"
                                            (assert)
                                            (("2"
                                              (replace -1)
                                              (("2"
                                                (case-replace
                                                 "u!1 - v!1 = zero")
                                                (("1" (assertnil nil)
                                                 ("2"
                                                  (lemma "norm_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)
   ((dist const-decl "nnreal" distance_2D 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)
    (Vect2 type-eq-decl nil vectors_2D_def nil)
    (nnreal type-eq-decl nil real_types nil)
    (sq_dist const-decl "nnreal" distance_2D nil)
    (Vector type-eq-decl nil vectors_2D nil)
    (+ const-decl "Vector" vectors_2D nil)
    (* const-decl "Vector" vectors_2D nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (- const-decl "Vector" vectors_2D nil)
    (* const-decl "real" vectors_2D nil)
    (norm_eq_0 formula-decl nil vectors_2D nil)
    (dot_zero_right formula-decl nil vectors_2D nil)
    (zero const-decl "Vector" vectors_2D nil)
    (dot_scal_left formula-decl nil vectors_2D 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_2D nil)
    (sqrt_eq formula-decl nil sqrt "reals/"))
   nil))
 (dot_nneg_tca_npos 0
  (dot_nneg_tca_npos-1 nil 3406984678
   ("" (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_2D nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (Vect2 type-eq-decl nil vectors_2D_def nil)
    (- const-decl "Vector" vectors_2D nil)
    (Vector type-eq-decl nil vectors_2D nil)
    (real nonempty-type-from-decl nil reals nil)
    (norm_eq_0 formula-decl nil vectors_2D 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 "Vect2" closest_approach_2D nil)
    (u!1 skolem-const-decl "Vect2" closest_approach_2D nil)
    (norm const-decl "nnreal" vectors_2D 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_2D 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 3409338501
   ("" (skosimp) (("" (replaces -2) (("" (grind) nil nil)) nil)) nil)
   ((sq const-decl "nonneg_real" sq "reals/")
    (sq_dist const-decl "nnreal" distance_2D nil)
    (dist const-decl "nnreal" distance_2D nil)
    (* const-decl "Vector" vectors_2D nil)
    (+ const-decl "Vector" vectors_2D nil)
    (divergent? const-decl "bool" closest_approach_2D 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))
 (dot_nneg_divergent 0
  (dot_nneg_divergent-1 nil 3406991840
   ("" (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_2D nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (divergent? const-decl "bool" closest_approach_2D nil)
    (time_closest const-decl "real" closest_approach_2D nil)
    (- const-decl "Vector" vectors_2D nil)
    (Vector type-eq-decl nil vectors_2D nil)
    (norm_eq_0 formula-decl nil vectors_2D nil)
    (sub_eq_zero formula-decl nil vectors_2D nil)
    (add_zero_right formula-decl nil vectors_2D nil)
    (scal_0 formula-decl nil vectors_2D 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_2D nil)
    (Vect2 type-eq-decl nil vectors_2D_def nil)
    (real nonempty-type-from-decl nil reals nil))
   nil))
 (divergent_dot_nneg 0
  (divergent_dot_nneg-1 nil 3411903197
   ("" (skosimp)
    (("" (case "divergent?(p0!1-q0!1,zero,u!1-v!1,zero)")
      (("1" (hide -2)
        (("1" (case "norm(u!1-v!1) /= 0")
          (("1" (flatten)
            (("1" (name-replace "s" "p0!1-q0!1")
              (("1" (name-replace "w" "u!1-v!1")
                (("1" (expand "divergent?")
                  (("1" (name "myt" "-(s*w)/sqv(w)")
                    (("1" (case "myt > 0")
                      (("1" (inst -3 "myt")
                        (("1" (expand "dist")
                          (("1" (rewrite "sqrt_lt")
                            (("1" (expand "sq_dist")
                              (("1"
                                (expand"*" "+")
                                (("1"
                                  (sq-simp)
                                  (("1"
                                    (move-terms -3 l)
                                    (("1"
                                      (assert)
                                      (("1"
                                        (expand "sq")
                                        (("1"
                                          (factor -3)
                                          (("1"
                                            (grind-reals
                                             -3
                                             :dontdistrib
                                             *)
                                            (("1"
                                              (move-terms -3 r (1 2))
                                              (("1"
                                                (add-formulas 2 -3)
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (factor 1)
                                                    (("1"
                                                      (replaces
                                                       -2
                                                       :dir
                                                       rl)
                                                      (("1"
                                                        (field 1)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (assertnil nil))
                        nil)
                       ("2" (hide -2)
                        (("2" (replaces -1 :dir rl)
                          (("2" (expand "norm")
                            (("2" (case-replace "sqv(w) = 0")
                              (("1" (rewrite "sqrt_0"nil nil)
                               ("2"
                                (cross-mult 2)
                                (("2" (assertnil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (flatten)
                      (("2" (hide -2 2)
                        (("2" (expand "norm")
                          (("2" (replaces -1)
                            (("2" (rewrite "sqrt_0"nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil)
           ("2" (flatten)
            (("2" (rewrite "norm_eq_0")
              (("2" (lemma "divergent_u_neq_v")
                (("2" (inst?) (("2" (assertnil nil)) nil)) nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (hide-all-but (-1 1))
        (("2" (expand "divergent?")
          (("2" (skosimp 1)
            (("2" (inst -1 "t!1")
              (("2" (assert)
                (("2" (expand "dist")
                  (("2" (rewrite "sqrt_lt")
                    (("2" (rewrite "sqrt_lt")
                      (("2" (expand "sq_dist")
                        (("2" (assert)
                          (("2" (expand"*" "+" "-")
                            (("2" (assertnil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((zero const-decl "Vector" vectors_2D nil)
    (- const-decl "Vector" vectors_2D nil)
    (Vector type-eq-decl nil vectors_2D nil)
    (divergent? const-decl "bool" closest_approach_2D nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (Vect2 type-eq-decl nil vectors_2D_def nil)
    (real nonempty-type-from-decl nil reals nil)
    (norm const-decl "nnreal" vectors_2D 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)
    (/= const-decl "boolean" notequal nil)
    (number nonempty-type-decl nil numbers nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (> const-decl "bool" reals nil)
    (dist const-decl "nnreal" distance_2D nil)
    (comp_zero_y formula-decl nil vectors_2D nil)
    (sq_times formula-decl nil sq "reals/")
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (sq_minus formula-decl nil sq "reals/")
    (nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (sq_0 formula-decl nil sq "reals/")
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (sq_plus formula-decl nil sq "reals/")
    (comp_zero_x formula-decl nil vectors_2D nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (div_cancel3 formula-decl nil real_props nil)
    (pos_times_lt formula-decl nil real_props nil)
    (IFF const-decl "[bool, bool -> bool]" booleans nil)
    (< const-decl "bool" reals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (add_zero_right formula-decl nil vectors_2D nil)
    (scal_zero formula-decl nil vectors_2D nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (sqrt_lt formula-decl nil sqrt "reals/")
    (sq_dist const-decl "nnreal" distance_2D nil)
    (+ const-decl "Vector" vectors_2D nil)
    (* const-decl "Vector" vectors_2D nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (myt skolem-const-decl "real" closest_approach_2D nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (sqrt_0 formula-decl nil sqrt "reals/")
    (w skolem-const-decl "Vector" closest_approach_2D nil)
    (div_mult_pos_gt1 formula-decl nil extra_real_props nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields 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_2D nil)
    (sqv const-decl "nnreal" vectors_2D nil)
    (norm_eq_0 formula-decl nil vectors_2D nil)
    (divergent_u_neq_v formula-decl nil closest_approach_2D nil))
   nil))
 (divergent_t1_lt_t2 0
  (divergent_t1_lt_t2-1 nil 3409356074
   ("" (skosimp)
    (("" (split)
      (("1" (flatten)
        (("1" (use "divergent_u_neq_v")
          (("1" (assert)
            (("1" (flatten)
              (("1" (skeep 2)
                (("1" (lemma "dist_diverges")
                  (("1"
                    (inst -1 "p0!1" "q0!1" "t1" "t2"
                     "time_closest(p0!1, q0!1, u!1, v!1)" "u!1" "v!1")
                    (("1" (beta)
                      (("1" (assert)
                        (("1" (hide 3)
                          (("1" (case "norm(u!1 - v!1) = 0")
                            (("1" (hide-all-but (-1 2))
                              (("1"
                                (rewrite "norm_eq_0")
                                (("1" (rewrite "sub_eq_zero"nil nil))
                                nil))
                              nil)
                             ("2" (assert)
                              (("2"
                                (lemma "dot_nneg_tca_npos")
                                (("2"
                                  (inst?)
                                  (("2"
                                    (assert)
                                    (("2"
                                      (use "divergent_dot_nneg")
                                      (("2" (assertnil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (flatten)
        (("2" (expand "divergent?")
          (("2" (skosimp)
            (("2" (inst -1 "0" "t!1") (("2" (assertnil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((divergent_u_neq_v formula-decl nil closest_approach_2D nil)
    (Vect2 type-eq-decl nil vectors_2D_def nil)
    (real nonempty-type-from-decl nil reals nil)
    (dist_diverges formula-decl nil closest_approach_2D nil)
    (divergent_dot_nneg formula-decl nil closest_approach_2D nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (dot_nneg_tca_npos formula-decl nil closest_approach_2D nil)
    (sub_eq_zero formula-decl nil vectors_2D nil)
    (norm_eq_0 formula-decl nil vectors_2D nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
--> --------------------

--> maximum size reached

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

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