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Datei: gs_only.prf   Sprache: Lisp

Original von: PVS©

(gs_only
 (k_l_det 0
  (k_l_det-2 nil 3441562959
   ("" (skeep)
    (("" (split +)
      (("1" (grind) nil nil)
       ("2" (rewrite "comps_eq")
        (("2" (flatten)
          (("2" (mult-by -1 "v`y")
            (("2" (mult-by -2 "v`x") (("2" (grind) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((det const-decl "real" det_2D "vectors/")
    (* const-decl "Vector" vectors_2D "vectors/")
    (+ const-decl "Vector" vectors_2D "vectors/")
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (both_sides_times1_imp formula-decl nil extra_real_props nil)
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (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)
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (real nonempty-type-from-decl nil reals nil)
    (comps_eq formula-decl nil vectors_2D "vectors/"))
   nil)
  (k_l_det-1 nil 3441562916 ("" (postpone) nil nilnil shostak))
 (k_l_det_nz 0
  (k_l_det_nz-1 nil 3441562983
   ("" (skeep)
    (("" (replaces -)
      (("" (grind) (("1" (field 2) nil nil) ("2" (field 2) nil nil))
        nil))
      nil))
    nil)
   ((= const-decl "[T, T -> boolean]" equalities nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (both_sides_times1 formula-decl nil real_props nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (div_cancel2 formula-decl nil real_props nil)
    (bijective? const-decl "bool" functions nil)
    (id const-decl "(bijective?[T, T])" identity nil)
    (TRUE const-decl "bool" booleans nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (/= const-decl "boolean" notequal nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real nonempty-type-from-decl nil reals nil)
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (- const-decl "Vector" vectors_2D "vectors/")
    (* const-decl "Vector" vectors_2D "vectors/")
    (det const-decl "real" det_2D "vectors/"))
   nil))
 (gs_only_line_k_l_TCC1 0
  (gs_only_line_k_l_TCC1-3 nil 3460224238
   ("" (skeep)
    (("" (skeep 2)
      (("" (skeep 2)
        (("" (case-replace "max(l,0)=l")
          (("1" (hide -1)
            (("1" (lemma "k_l_det_nz")
              (("1" (inst?) (("1" (assertnil nil)) nil)) nil))
            nil)
           ("2" (hide-all-but (-3 1)) (("2" (grind) nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (= const-decl "[T, T -> boolean]" equalities 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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (>= const-decl "bool" reals nil)
    (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
    (k_l_det_nz formula-decl nil gs_only nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil)
  (gs_only_line_k_l_TCC1-2 nil 3460222808
   ("" (skosimp*) (("" (assertnil nil)) nilnil nil)
  (gs_only_line_k_l_TCC1-1 nil 3460222678
   ("" (skeep)
    (("" (skeep 2) (("" (skeep 2) (("" (assertnil nil)) nil)) nil))
    nil)
   nil nil))
 (gs_only_line_k_l_TCC2 0
  (gs_only_line_k_l_TCC2-2 nil 3460222860
   ("" (skosimp*) (("" (assertnil nil)) nil)
   ((real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil)
  (gs_only_line_k_l_TCC2-1 nil 3460222678 ("" (subtype-tcc) nil nil)
   nil nil))
 (gs_only_line_k_l_complete 0
  (gs_only_line_k_l_complete-1 nil 3460223297
   ("" (skeep)
    (("" (case-replace "vo=zero")
      (("1" (rewrite "det_zero_left")
        (("1" (rewrite "det_zero_right") (("1" (assertnil nil)) nil))
        nil)
       ("2" (lemma "k_l_det")
        (("2" (inst -1 "k" "v" "vi" "vo" "l")
          (("2" (split -1)
            (("1" (flatten)
              (("1"
                (name-replace "gso" "gs_only_line_k_l(v,vo, vi)" :hide?
                 nil)
                (("1" (expand "gs_only_line_k_l")
                  (("1" (lift-if)
                    (("1" (split -1)
                      (("1" (flatten)
                        (("1" (div-by -2 "det(vo,v)")
                          (("1" (div-by -3 "det(vo,v)")
                            (("1" (replaces (-2 -3) :dir rl)
                              (("1"
                                (case-replace "max(l,0)=l")
                                (("1"
                                  (case-replace "max(l,0)=0")
                                  (("1" (assertnil nil)
                                   ("2"
                                    (hide-all-but (1 2))
                                    (("2" (grind) nil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil)
                       ("2" (flatten) (("2" (assertnil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (replaces -2)
              (("2" (hide-all-but 1) (("2" (assertnil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real nonempty-type-from-decl nil reals nil)
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (boolean nonempty-type-decl nil booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (zero const-decl "Vector" vectors_2D "vectors/")
    (det_zero_right formula-decl nil det_2D "vectors/")
    (sub_zero_left formula-decl nil vectors_2D "vectors/")
    (scal_zero formula-decl nil vectors_2D "vectors/")
    (det_zero_left formula-decl nil det_2D "vectors/")
    (number nonempty-type-decl nil numbers 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)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (add_cancel2 formula-decl nil vectors_2D "vectors/")
    (real_times_real_is_real application-judgement "real" reals nil)
    (both_sides_div1 formula-decl nil real_props nil)
    (/= const-decl "boolean" notequal nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (det const-decl "real" det_2D "vectors/")
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (times_div_cancel2 formula-decl nil extra_real_props nil)
    (max_nnreal_0 formula-decl nil min_max "reals/")
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nonneg_real_max application-judgement
     "{z: nonneg_real | z >= x AND z >= y}" real_defs nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
    (gs_only_line_k_l const-decl
     "{k: real, l: nnreal | l > 0 => k * v = l * vo - vi}" gs_only nil)
    (- const-decl "Vector" vectors_2D "vectors/")
    (* const-decl "Vector" vectors_2D "vectors/")
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (nnreal type-eq-decl nil real_types nil)
    (k_l_det formula-decl nil gs_only nil))
   nil))
 (gs_only_line_TCC1 0
  (gs_only_line_TCC1-2 nil 3443969346
   ("" (skeep)
    (("" (case-replace "l=0")
      (("1" (assertnil nil)
       ("2" (rewrite "gs_only_scal")
        (("2" (typepred "gs_only_line_k_l(v,vo,vi)")
          (("2" (assertnil nil)) nil))
        nil))
      nil))
    nil)
   ((number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nnreal type-eq-decl nil real_types nil)
    (scal_0 formula-decl nil vectors_2D "vectors/")
    (gs_only_line_k_l const-decl
     "{k: real, l: nnreal | l > 0 => k * v = l * vo - vi}" gs_only nil)
    (- const-decl "Vector" vectors_2D "vectors/")
    (* const-decl "Vector" vectors_2D "vectors/")
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (NOT const-decl "[bool -> bool]" booleans 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)
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (gs_only_scal formula-decl nil definitions nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil)
  (gs_only_line_TCC1-1 nil 3443969286 ("" (subtype-tcc) nil nilnil
   nil))
 (same_gs_only_line 0
  (same_gs_only_line-1 nil 3443962519
   ("" (skeep)
    (("" (expand "gs_only_line")
      (("" (expand "gs_only_line_k_l")
        (("" (replaces -1)
          (("" (rewrite "det_scal_left")
            (("" (name-replace "dvi" "det(vi,v)")
              (("" (name-replace "dv1" "det(v1,v)")
                (("" (case "dv1 = 0")
                  (("1" (assertnil nil)
                   ("2" (assert)
                    (("2" (copy 1)
                      (("2" (mult-by 1 "l")
                        (("2" (assert)
                          (("2"
                            (case-replace
                             "dvi/(l*dv1) = (1/l)*(dvi/dv1)")
                            (("1" (hide -1)
                              (("1"
                                (lemma "nneg_mult_max")
                                (("1"
                                  (inst -1 "1/l" "dvi/dv1" "0")
                                  (("1" (assertnil nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (assertnil nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((gs_only_line const-decl "{k: real, nvo: Vect2 |
         nvo /= zero => gs_only?(vo)(nvo) AND k * v = nvo - vi}"
     gs_only nil)
    (det const-decl "real" det_2D "vectors/")
    (= const-decl "[T, T -> boolean]" equalities nil)
    (scal_0 formula-decl nil vectors_2D "vectors/")
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (nnreal type-eq-decl nil real_types nil)
    (nneg_mult_max formula-decl nil min_max "reals/")
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types 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 -> numfield]" number_fields nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (/= const-decl "boolean" notequal nil)
    (both_sides_times1 formula-decl nil real_props nil)
    (scal_assoc formula-decl nil vectors_2D "vectors/")
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (det_scal_left formula-decl nil det_2D "vectors/")
    (gs_only_line_k_l const-decl
     "{k: real, l: nnreal | l > 0 => k * v = l * vo - vi}" gs_only
     nil))
   nil))
 (gs_only_line_complete 0
  (gs_only_line_complete-1 nil 3443983668
   ("" (skeep)
    (("" (expand "gs_only_line?")
      (("" (case "nvo=zero")
        (("1" (replaces -1)
          (("1" (rewrite "gs_only_zero_right")
            (("1" (replaces -1)
              (("1" (rewrite "det_zero_left")
                (("1" (rewrite "det_zero_right")
                  (("1" (assertnil nil)) nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (assert)
          (("2" (expand "gs_only?")
            (("2" (skeep -1)
              (("2" (lemma "gs_only_line_k_l_complete")
                (("2" (inst?)
                  (("2" (inst?)
                    (("2" (inst?)
                      (("2" (assert)
                        (("2" (split -1)
                          (("1" (expand "gs_only_line")
                            (("1" (replaces -1 :dir rl)
                              (("1" (assertnil nil)) nil))
                            nil)
                           ("2" (propax) nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((gs_only_line? const-decl "bool" gs_only nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (gs_only_line const-decl "{k: real, nvo: Vect2 |
         nvo /= zero => gs_only?(vo)(nvo) AND k * v = nvo - vi}"
     gs_only nil)
    (number nonempty-type-decl nil numbers 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)
    (gs_only_line_k_l_complete formula-decl nil gs_only nil)
    (gs_only? const-decl "bool" definitions nil)
    (det_zero_right formula-decl nil det_2D "vectors/")
    (sub_zero_left formula-decl nil vectors_2D "vectors/")
    (det_zero_left formula-decl nil det_2D "vectors/")
    (gs_only_zero_right formula-decl nil definitions nil)
    (real nonempty-type-from-decl nil reals nil)
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (boolean nonempty-type-decl nil booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (zero const-decl "Vector" vectors_2D "vectors/"))
   nil))
 (gs_only_dot_TCC1 0
  (gs_only_dot_TCC1-2 nil 3445697631
   ("" (skeep)
    ((""
      (name-replace "gso"
       "gs_only_line(Vdir(u, vo - vi), vo, vi + W0(u, j))")
      (("" (typepred "gso")
        (("" (assert)
          (("" (flatten)
            (("" (assert)
              ((""
                (case "W0(u,j) + gso`1 * Vdir(u, vo - vi) = gso`2 - vi")
                (("1" (replaces -1 :dir rl)
                  (("1" (rewrite "W_dot"nil nil)) nil)
                 ("2" (replaces -2)
                  (("2" (hide-all-but 1)
                    (("2" (grind :exclude "W0"nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    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)
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (= const-decl "[T, T -> boolean]" equalities nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (/= const-decl "boolean" notequal nil)
    (zero const-decl "Vector" vectors_2D "vectors/")
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (gs_only? const-decl "bool" definitions nil)
    (* const-decl "Vector" vectors_2D "vectors/")
    (- const-decl "Vector" vectors_2D "vectors/")
    (gs_only_line const-decl "{k: real, nvo: Vect2 |
         nvo /= zero => gs_only?(vo)(nvo) AND k * v = nvo - vi}"
     gs_only nil)
    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (Vdir const-decl "Nz_vect2" definitions nil)
    (+ const-decl "Vector" vectors_2D "vectors/")
    (W0 const-decl "Vect2" definitions nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (W_dot formula-decl nil definitions nil)
    (NOT const-decl "[bool -> bool]" booleans nil))
   nil)
  (gs_only_dot_TCC1-1 nil 3445697622 ("" (subtype-tcc) nil nilnil
   nil))
 (gs_only_dot_complete 0
  (gs_only_dot_complete-1 nil 3459320682
   ("" (skeep)
    (("" (case "nvo=zero")
      (("1" (expand "gs_only?")
        (("1" (replaces -1)
          (("1" (skeep -1) (("1" (assertnil nil)) nil)) nil))
        nil)
       ("2" (expand "gs_only_dot")
        (("2" (lemma "dot_W")
          (("2" (inst? -1)
            (("2" (inst? -1)
              (("2" (assert)
                (("2" (skeep -1)
                  (("2" (lemma "gs_only_line_complete")
                    (("2" (expand "gs_only_line?")
                      (("2"
                        (inst -1 "k" "nvo" "Vdir(u,vnzo-vi)"
                         "vi+W0(u,j)" "vnzo")
                        (("2" (assert)
                          (("2" (split)
                            (("1" (propax) nil nil)
                             ("2" (hide-all-but (-1 1))
                              (("2"
                                (grind :exclude ("W0" "Vdir"))
                                nil
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((zero const-decl "Vector" vectors_2D "vectors/")
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (= const-decl "[T, T -> boolean]" equalities nil)
    (boolean nonempty-type-decl nil booleans nil)
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (real nonempty-type-from-decl nil reals nil)
    (nz_nzv application-judgement "Nz_vector" vectors_2D "vectors/")
    (gs_only? const-decl "bool" definitions nil)
    (dot_W formula-decl nil definitions nil)
    (gs_only_line? const-decl "bool" gs_only nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (* const-decl "Vector" vectors_2D "vectors/")
    (Vdir const-decl "Nz_vect2" definitions nil)
    (+ const-decl "Vector" vectors_2D "vectors/")
    (W0 const-decl "Vect2" definitions nil)
    (gs_only_line_complete formula-decl nil gs_only nil)
    (- const-decl "Vector" vectors_2D "vectors/")
    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (/= const-decl "boolean" notequal nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number nonempty-type-decl nil numbers nil)
    (gs_only_dot const-decl
     "{nvo | nvo /= zero => gs_only?(vo)(nvo) AND u * (nvo - vi) = j}"
     gs_only nil))
   nil))
 (gs_only_circle_TCC1 0
  (gs_only_circle_TCC1-2 nil 3459321977
   ("" (skeep)
    (("" (skeep)
      (("" (skeep)
        (("" (skeep)
          (("" (skeep)
            (("" (skeep)
              (("" (case "l>0")
                (("1" (expand "max")
                  (("1" (assert)
                    (("1" (hide-all-but (-1 -9 2))
                      (("1" (replaces -2)
                        (("1" (rewrite "gs_only_scal"nil nil)) nil))
                      nil))
                    nil))
                  nil)
                 ("2" (hide-all-but (-8 1 2))
                  (("2" (case-replace "max(l,0)=0")
                    (("1" (assertnil nil)
                     ("2" (hide-all-but (1 2)) (("2" (grind) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((scal_0 formula-decl nil vectors_2D "vectors/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (gs_only_scal formula-decl nil definitions nil)
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (/= const-decl "boolean" notequal nil)
    (zero const-decl "Vector" vectors_2D "vectors/")
    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (>= const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (sq_nz_pos application-judgement "posreal" sq "reals/")
    (nz_sqv_gt_0 application-judgement "posreal" vectors_2D "vectors/")
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props 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))
   nil)
  (gs_only_circle_TCC1-1 nil 3459321845 ("" (subtype-tcc) nil nilnil
   nil))
 (gs_only_circle_TCC2 0
  (gs_only_circle_TCC2-1 nil 3461670291 ("" (skosimp*) nil nilnil
   nil))
 (gs_only_circle_TCC3 0
  (gs_only_circle_TCC3-1 nil 3461670291 ("" (skosimp*) nil nilnil
   nil))
 (gs_only_circle_solution 0
  (gs_only_circle_solution-2 nil 3565275328
   ("" (skeep)
    (("" (expand "circle_solution_2D?")
      (("" (expand "gs_only_circle?")
        (("" (flatten)
          (("" (skeep -1)
            (("" (expand "gs_only_circle" :assert? none)
              (("" (skoletin* -1 :old? t)
                (("" (lift-if)
                  (("" (split -2)
                    (("1" (flatten)
                      (("1" (skoletin* -2 :postfix "p" :old? t)
                        (("1" (case "lp > 0")
                          (("1" (expand "max")
                            (("1" (assert)
                              (("1"
                                (lift-if)
                                (("1"
                                  (split -3)
                                  (("1"
                                    (flatten)
                                    (("1"
                                      (assert)
                                      (("1"
                                        (lemma "quad2b_eq_0")
                                        (("1"
                                          (inst? -1)
                                          (("1"
                                            (inst -1 "lp")
                                            (("1"
                                              (flatten)
                                              (("1"
                                                (hide -1)
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (split -1)
                                                    (("1"
                                                      (replaces
                                                       (-3 -5))
                                                      (("1"
                                                        (hide-all-but
                                                         (-1
                                                          -6
                                                          -7
                                                          -8
                                                          -9
                                                          2))
                                                        (("1"
                                                          (grind)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil)
                                                     ("2"
                                                      (inst 1 "irt")
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2" (flatten) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (case-replace "max(lp,0)=0")
                            (("1" (assert)
                              (("1"
                                (lift-if)
                                (("1"
                                  (split -3)
                                  (("1"
                                    (flatten)
                                    (("1" (assertnil nil))
                                    nil)
                                   ("2" (flatten) nil nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (hide-all-but (1 2))
                              (("2" (grind) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (flatten) nil nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((circle_solution_2D? const-decl "bool" horizontal nil)
    (gs_only_circle const-decl
     "{nvo | nvo /= zero => gs_only?(vnzo)(nvo)}" gs_only nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (quadratic const-decl "real" quadratic "reals/")
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (quad2b_eq_0 formula-decl nil quadratic_2b "reals/")
    (scal_0 formula-decl nil vectors_2D "vectors/")
    (bijective? const-decl "bool" functions nil)
    (id const-decl "(bijective?[T, T])" identity nil)
    (TRUE const-decl "bool" booleans nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (/= const-decl "boolean" notequal nil)
    (nzreal nonempty-type-eq-decl nil reals nil)
    (discr2b const-decl "real" quadratic_2b "reals/")
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nzint nonempty-type-eq-decl nil integers nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (Sign type-eq-decl nil sign "reals/")
    (* const-decl "real" vectors_2D "vectors/")
    (+ const-decl "Vector" vectors_2D "vectors/")
    (zero const-decl "Vector" vectors_2D "vectors/")
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (root2b const-decl "real" quadratic_2b "reals/")
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (nnreal type-eq-decl nil real_types nil)
    (sqv const-decl "nnreal" vectors_2D "vectors/")
    (sq const-decl "nonneg_real" sq "reals/")
    (D formal-const-decl "posreal" gs_only nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (* const-decl "Vector" vectors_2D "vectors/")
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number nonempty-type-decl nil numbers nil)
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (- const-decl "Vector" vectors_2D "vectors/")
    (= const-decl "[T, T -> boolean]" equalities nil)
    (boolean nonempty-type-decl nil booleans nil)
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (real nonempty-type-from-decl nil reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (sq_nz_pos application-judgement "posreal" sq "reals/")
    (IFF const-decl "[bool, bool -> bool]" booleans nil)
    (nz_sqv_gt_0 application-judgement "posreal" vectors_2D "vectors/")
    (gs_only_circle? const-decl "bool" gs_only nil))
   nil)
  (gs_only_circle_solution-1 nil 3461670946
   ("" (skeep)
    (("" (expand "circle_solution_2D?")
      (("" (expand "gs_only_circle?")
        (("" (flatten)
          (("" (skeep -1)
            (("" (expand "gs_only_circle" :assert? none)
              (("" (skoletin* -1)
                (("" (lift-if)
                  (("" (split -2)
                    (("1" (flatten)
                      (("1" (skoletin* -2 :postfix "p")
                        (("1" (case "lp > 0")
                          (("1" (expand "max")
                            (("1" (assert)
                              (("1"
                                (lift-if)
                                (("1"
                                  (split -3)
                                  (("1"
                                    (flatten)
                                    (("1"
                                      (assert)
                                      (("1"
                                        (lemma "quad2b_eq_0")
                                        (("1"
                                          (inst? -1)
                                          (("1"
                                            (inst -1 "lp")
                                            (("1"
                                              (flatten)
                                              (("1"
                                                (hide -1)
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (split -1)
                                                    (("1"
                                                      (replaces
                                                       (-3 -5))
                                                      (("1"
                                                        (hide-all-but
                                                         (-1
                                                          -6
                                                          -7
                                                          -8
                                                          -9
                                                          2))
                                                        (("1"
                                                          (grind)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil)
                                                     ("2"
                                                      (inst 1 "irt")
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2" (flatten) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (case-replace "max(lp,0)=0")
                            (("1" (assert)
                              (("1"
                                (lift-if)
                                (("1"
                                  (split -3)
                                  (("1"
                                    (flatten)
                                    (("1" (assertnil nil))
                                    nil)
                                   ("2" (flatten) nil nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (hide-all-but (1 2))
                              (("2" (grind) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (flatten) nil nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((circle_solution_2D? const-decl "bool" horizontal nil)
    (quadratic const-decl "real" quadratic "reals/")
    (quad2b_eq_0 formula-decl nil quadratic_2b "reals/")
    (scal_0 formula-decl nil vectors_2D "vectors/")
    (sq const-decl "nonneg_real" sq "reals/")
    (sqv const-decl "nnreal" vectors_2D "vectors/")
    (root2b const-decl "real" quadratic_2b "reals/")
    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (zero const-decl "Vector" vectors_2D "vectors/")
    (+ const-decl "Vector" vectors_2D "vectors/")
    (* const-decl "real" vectors_2D "vectors/")
    (Sign type-eq-decl nil sign "reals/")
    (discr2b const-decl "real" quadratic_2b "reals/")
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (* const-decl "Vector" vectors_2D "vectors/")
    (sq_nz_pos application-judgement "posreal" sq "reals/")
    (nz_sqv_gt_0 application-judgement "posreal" vectors_2D
     "vectors/"))
   nil))
 (gs_only_circle_complete 0
  (gs_only_circle_complete-1 nil 3459321586
   ("" (skeep)
    (("" (expand "circle_solution_2D?")
      (("" (flatten)
        (("" (expand "gs_only_circle?")
          (("" (case-replace "nvo=zero")
            (("1" (rewrite "gs_only_zero_right"nil nil)
             ("2" (assert)
              (("2" (expand "gs_only?")
                (("2" (skeep -1)
                  (("2" (lemma "quad2b_eq_0")
                    (("2" (name "w" "s-t*vi")
                      (("2" (name "a" "sq(t)*sqv(vnzo)")
                        (("2" (name "b" "t*(w*vnzo)")
                          (("2" (name "c" "sqv(w)-sq(D)")
                            (("2" (inst -5 "a" "b" "c" "l")
                              (("2"
                                (flatten)
                                (("2"
                                  (hide -6)
                                  (("2"
                                    (split -5)
                                    (("1"
                                      (flatten)
                                      (("1"
                                        (skeep -2)
                                        (("1"
                                          (inst 2 "eps")
                                          (("1"
                                            (expand "gs_only_circle")
                                            (("1"
                                              (replaces
                                               :from
                                               -6
                                               :to
                                               -3)
                                              (("1"
                                                (assert)
                                                (("1"
                                                  (replaces -2 :dir rl)
                                                  (("1"
                                                    (case-replace
                                                     "max(l,0)=l")
                                                    (("1"
                                                      (assert)
                                                      nil
                                                      nil)
                                                     ("2"
                                                      (case
                                                       "max(l,0)=0")
                                                      (("1"
                                                        (assert)
                                                        nil
                                                        nil)
                                                       ("2"
                                                        (hide-all-but
                                                         (1 2))
                                                        (("2"
                                                          (grind)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (hide -7 2 3)
                                      (("2" (grind) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((circle_solution_2D? const-decl "bool" horizontal nil)
    (gs_only_circle? const-decl "bool" gs_only nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (sq_nz_pos application-judgement "posreal" sq "reals/")
    (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)
    (* const-decl "Vector" vectors_2D "vectors/")
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number nonempty-type-decl nil numbers nil)
    (- const-decl "Vector" vectors_2D "vectors/")
    (* const-decl "real" vectors_2D "vectors/")
    (nzreal nonempty-type-eq-decl nil reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (+ const-decl "Vector" vectors_2D "vectors/")
    (quadratic const-decl "real" quadratic "reals/")
    (Sign type-eq-decl nil sign "reals/")
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (nzint nonempty-type-eq-decl nil integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (nz_nzv application-judgement "Nz_vector" vectors_2D "vectors/")
    (max_nnreal_0 formula-decl nil min_max "reals/")
    (gs_only_circle const-decl
     "{nvo | nvo /= zero => gs_only?(vnzo)(nvo)}" gs_only nil)
    (nz_sqv_gt_0 application-judgement "posreal" vectors_2D "vectors/")
    (D formal-const-decl "posreal" gs_only nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (sqv const-decl "nnreal" vectors_2D "vectors/")
    (nnreal type-eq-decl nil real_types nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (quad2b_eq_0 formula-decl nil quadratic_2b "reals/")
    (gs_only? const-decl "bool" definitions nil)
    (gs_only_zero_right formula-decl nil definitions nil)
    (/= const-decl "boolean" notequal nil)
    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (zero const-decl "Vector" vectors_2D "vectors/")
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (= const-decl "[T, T -> boolean]" equalities nil)
    (boolean nonempty-type-decl nil booleans nil)
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (real nonempty-type-from-decl nil reals nil))
   nil))
 (gs_only_vertical_TCC1 0
  (gs_only_vertical_TCC1-1 nil 3471002852
   ("" (skeep)
    (("" (lemma "Delta_gt_0_nzv")
      (("" (inst?) (("" (assertnil nil)) nil)) nil))
    nil)
   ((D formal-const-decl "posreal" gs_only nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (Delta_gt_0_nzv formula-decl nil horizontal nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/"))
   nil))
 (gs_only_vertical_TCC2 0
  (gs_only_vertical_TCC2-3 nil 3471110192
   ("" (skeep)
    (("" (skeep)
      (("" (lemma "scal_eq_zero")
        (("" (inst?)
          (("" (assert)
            (("" (rewrite "sqv_eq_0" :dir rl)
              (("" (replaces -5)
                (("" (lemma "Theta_D_on_D")
                  (("" (inst?)
                    (("" (assert) (("" (assertnil nil)) nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (sqv_eq_0 formula-decl nil vectors_2D "vectors/")
    (Theta_D_on_D formula-decl nil horizontal nil)
    (D formal-const-decl "posreal" gs_only nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (sq_nz_pos application-judgement "posreal" sq "reals/")
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (zero const-decl "Vector" vectors_2D "vectors/")
    (Sign type-eq-decl nil sign "reals/")
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (nzint nonempty-type-eq-decl nil integers nil)
    (/= const-decl "boolean" notequal nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (scal_eq_zero formula-decl nil vectors_2D "vectors/"))
   nil)
  (gs_only_vertical_TCC2-2 nil 3471022326
   ("" (skeep)
    (("" (skeep)
      (("" (skeep)
        (("" (skeep 2)
          (("" (expand "gs_only?")
            (("" (inst? 3)
              (("" (rewrite "max_gt")
                (("" (case-replace "max(k,0)=0")
                  (("1" (assertnil nil)
                   ("2" (hide-all-but (1 2)) (("2" (grind) nil nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((gs_only? const-decl "bool" definitions nil)
    (scal_0 formula-decl nil vectors_2D "vectors/"))
   nil)
  (gs_only_vertical_TCC2-1 nil 3471002852
   ("" (skosimp*) (("" (postpone) nil nil)) nilnil nil))
 (gs_only_vertical_TCC3 0
  (gs_only_vertical_TCC3-1 nil 3471021482
   ("" (skeep)
    (("" (skeep)
      (("" (typepred "gs_only_dot(t * p, vo, vi, sq(D) - s * p)")
        (("" (assertnil nil)) nil))
      nil))
    nil)
   ((dot_scal_left formula-decl nil vectors_2D "vectors/")
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (real nonempty-type-from-decl nil reals nil)
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (/= const-decl "boolean" notequal nil)
    (zero const-decl "Vector" vectors_2D "vectors/")
    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (number nonempty-type-decl nil numbers 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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (gs_only? const-decl "bool" definitions nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (* const-decl "real" vectors_2D "vectors/")
    (- const-decl "Vector" vectors_2D "vectors/")
    (gs_only_dot const-decl
     "{nvo | nvo /= zero => gs_only?(vo)(nvo) AND u * (nvo - vi) = j}"
     gs_only nil)
    (* const-decl "Vector" vectors_2D "vectors/")
    (>= const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (sq const-decl "nonneg_real" sq "reals/")
    (D formal-const-decl "posreal" gs_only nil)
    (sq_nz_pos application-judgement "posreal" sq "reals/"))
   nil))
 (gs_only_vertical_TCC4 0
  (gs_only_vertical_TCC4-1 nil 3471021482 ("" (skosimp*) nil nilnil
   nil))
 (gs_only_vertical_on_D 0
  (gs_only_vertical_on_D-1 nil 3471022777
   ("" (skeep)
    (("" (beta)
      (("" (flatten)
        (("" (expand "gs_only_vertical?")
          (("" (flatten)
            (("" (expand "gs_only_vertical")
              (("" (lift-if)
                (("" (split -1)
                  (("1" (flatten)
                    (("1" (assert)
                      (("1"
                        (typepred
                         "gs_only_dot(t * (s + Theta_D(s, vo - vi, dir) * (vo - vi)), vo, vi,
                   sq(D) - s * (s + Theta_D(s, vo - vi, dir) * (vo - vi)))")
                        (("1" (replaces -4 :dir rl)
                          (("1" (assert)
                            (("1" (flatten)
                              (("1"
                                (hide-all-but (-2 2))
                                (("1"
                                  (grind :exclude "Theta_D")
                                  nil
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (flatten) nil nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((gs_only_vertical? const-decl "bool" gs_only nil)
    (sq_nz_pos application-judgement "posreal" sq "reals/")
    (gs_only_vertical const-decl
     "{nvo | nvo /= zero => gs_only?(vo)(nvo)}" gs_only nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (dot_scal_left formula-decl nil vectors_2D "vectors/")
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (real nonempty-type-from-decl nil reals nil)
    (Vector type-eq-decl nil vectors_2D "vectors/")
    (/= const-decl "boolean" notequal nil)
    (zero const-decl "Vector" vectors_2D "vectors/")
    (Nz_vect2 type-eq-decl nil vectors_2D "vectors/")
    (Vect2 type-eq-decl nil vectors_2D_def "vectors/")
    (number nonempty-type-decl nil numbers 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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (gs_only? const-decl "bool" definitions nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (* const-decl "real" vectors_2D "vectors/")
    (- const-decl "Vector" vectors_2D "vectors/")
    (gs_only_dot const-decl
     "{nvo | nvo /= zero => gs_only?(vo)(nvo) AND u * (nvo - vi) = j}"
     gs_only nil)
    (* const-decl "Vector" vectors_2D "vectors/")
    (>= const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (+ const-decl "Vector" vectors_2D "vectors/")
    (D formal-const-decl "posreal" gs_only nil)
    (Delta const-decl "real" horizontal nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nzint nonempty-type-eq-decl nil integers nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (Sign type-eq-decl nil sign "reals/")
    (Theta_D const-decl "real" horizontal nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (sq const-decl "nonneg_real" sq "reals/"))
   nil)))


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