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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei:   Sprache: Lisp

Original von: PVS©

(limit_vect_real
 (cv_unique 0
  (cv_unique-2 nil 3442578793
   ("" (grind :exclude ("abs" "norm" "-" "sigma") :if-match nil)
    (("" (rewrite "abs_diff_0")
      (("" (name "eps" "abs(l1!1 - l2!1)")
        (("" (replace -1)
          (("" (inst -4 "eps/2")
            (("1" (inst -5 "eps/2")
              (("1" (assert)
                (("1" (skosimp*)
                  (("1"
                    (case " EXISTS (x: Vector): a!1 /= x AND norm(x - a!1) < delta!1 AND norm(x - a!1) < delta!2")
                    (("1" (skosimp*)
                      (("1" (inst?)
                        (("1" (inst?)
                          (("1" (assert)
                            (("1" (case "0 < norm(x!1 - a!1)")
                              (("1"
                                (assert)
                                (("1"
                                  (lemma "triangle2")
                                  (("1"
                                    (inst
                                     -
                                     "eps/2"
                                     "eps/2"
                                     "l1!1"
                                     "f!1(x!1)"
                                     "l2!1")
                                    (("1" (assertnil nil))
                                    nil))
                                  nil))
                                nil)
                               ("2"
                                (lemma "norm_eq_0")
                                (("2"
                                  (inst?)
                                  (("2"
                                    (assert)
                                    (("2"
                                      (replace -1 * lr)
                                      (("2"
                                        (assert)
                                        (("2"
                                          (rewrite "sub_eq_zero")
                                          nil
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (hide -4 -5)
                      (("2" (name "DEL" "min(delta!1,delta!2)")
                        (("2"
                          (name AA "a!1 WITH [0 := a!1(0) + DEL/2]")
                          (("1" (inst + "AA")
                            (("1" (case "norm(AA - a!1) = abs(DEL/2)")
                              (("1"
                                (replace -1 * lr)
                                (("1"
                                  (hide -1)
                                  (("1"
                                    (case "a!1 /= AA")
                                    (("1"
                                      (assert)
                                      (("1"
                                        (hide -1 -2)
                                        (("1" (grind) nil nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (flatten)
                                      (("2"
                                        (assert)
                                        (("2"
                                          (hide 1 -3 -4)
                                          (("2"
                                            (replace -1 * lr)
                                            (("2"
                                              (hide -1)
                                              (("2"
                                                (case
                                                 "AA WITH [(0) := AA(0) + DEL / 2](0) = AA(0)")
                                                (("1"
                                                  (hide -2)
                                                  (("1"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (replace -1 * lr)
                                                  (("2"
                                                    (propax)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil)
                               ("2"
                                (hide -1)
                                (("2"
                                  (reveal -1)
                                  (("2"
                                    (hide 2)
                                    (("2"
                                      (replace -1 * rl)
                                      (("2"
                                        (hide -1)
                                        (("2"
                                          (expand "norm")
                                          (("2"
                                            (case-replace
                                             "a!1 WITH [(0) := a!1(0) + DEL / 2] - a!1 =
                                     (LAMBDA (i: Index): IF i = 0 THEN DEL/2 ELSE 0 ENDIF)")
                                            (("1"
                                              (hide -1)
                                              (("1"
                                                (expand "sqv")
                                                (("1"
                                                  (expand "*")
                                                  (("1"
                                                    (lemma
                                                     "sigma_first")
                                                    (("1"
                                                      (inst?)
                                                      (("1"
                                                        (assert)
                                                        (("1"
                                                          (assert)
                                                          (("1"
                                                            (replace
                                                             -1)
                                                            (("1"
                                                              (hide -1)
                                                              (("1"
                                                                (lemma
                                                                 "sigma_restrict")
                                                                (("1"
                                                                  (inst?)
                                                                  (("1"
                                                                    (assert)
                                                                    (("1"
                                                                      (inst
                                                                       -
                                                                       "n-1"
                                                                       "1")
                                                                      (("1"
                                                                        (assert)
                                                                        (("1"
                                                                          (replace
                                                                           -1
                                                                           *
                                                                           lr)
                                                                          (("1"
                                                                            (hide
                                                                             -1)
                                                                            (("1"
                                                                              (expand
                                                                               "restrict")
                                                                              (("1"
                                                                                (rewrite
                                                                                 "sigma_const")
                                                                                (("1"
                                                                                  (assert)
                                                                                  (("1"
                                                                                    (expand
                                                                                     "abs")
                                                                                    (("1"
                                                                                      (propax)
                                                                                      nil
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (assert)
                                                                        (("2"
                                                                          (case
                                                                           "n = 1")
                                                                          (("1"
                                                                            (replace
                                                                             -1)
                                                                            (("1"
                                                                              (expand
                                                                               "sigma")
                                                                              (("1"
                                                                                (assert)
                                                                                (("1"
                                                                                  (expand
                                                                                   "abs")
                                                                                  (("1"
                                                                                    (propax)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (case-replace
                                                                             "n = 0")
                                                                            (("1"
                                                                              (assert)
                                                                              nil
                                                                              nil)
                                                                             ("2"
                                                                              (assert)
                                                                              nil
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("2"
                                              (apply-extensionality
                                               1
                                               :hide?
                                               t)
                                              (("2"
                                                (assert)
                                                (("2"
                                                  (hide 2)
                                                  (("2"
                                                    (lift-if)
                                                    (("2"
                                                      (ground)
                                                      (("1"
                                                        (replace -1)
                                                        (("1"
                                                          (assert)
                                                          (("1"
                                                            (expand
                                                             "-")
                                                            (("1"
                                                              (propax)
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil)
                                                       ("2"
                                                        (expand "-")
                                                        (("2"
                                                          (propax)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (assertnil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (assertnil nil))
              nil)
             ("2" (assertnil nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((abs_diff_0 formula-decl nil abs_lems "reals/")
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (nonzero_abs_is_pos application-judgement "{y: posreal | y >= x}"
     real_defs nil)
    (* const-decl "real" vectors "vectors/")
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (T_low type-eq-decl nil sigma "reals/")
    (T_high type-eq-decl nil sigma "reals/")
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (sigma_nat application-judgement "nat" limit_vect_real nil)
    (restrict const-decl "[T -> real]" sigma "reals/")
    (nnreal_plus_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (sqrt_pos application-judgement "posreal" sqrt "reals/")
    (sqrt_square formula-decl nil sqrt "reals/")
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (int_times_even_is_even application-judgement "even_int" integers
     nil)
    (sigma_const formula-decl nil sigma "reals/")
    (sigma def-decl "real" sigma "reals/")
    (sigma_nnreal application-judgement "nnreal" limit_vect_real nil)
    (sigma_restrict formula-decl nil sigma "reals/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (below type-eq-decl nil naturalnumbers nil)
    (sigma_first formula-decl nil sigma "reals/")
    (sqv const-decl "nnreal" vectors "vectors/")
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (<= const-decl "bool" reals nil)
    (posreal_min application-judgement
     "{z: posreal | z <= x AND z <= y}" real_defs nil)
    (triangle2 formula-decl nil abs_lems "reals/")
    (sub_eq_zero formula-decl nil vectors "vectors/")
    (norm_zero formula-decl nil vectors "vectors/")
    (norm_eq_0 formula-decl nil vectors "vectors/")
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (- const-decl "real" vectors "vectors/")
    (norm const-decl "nnreal" vectors "vectors/")
    (nnreal type-eq-decl nil real_types nil)
    (Vector type-eq-decl nil vectors "vectors/")
    (Index type-eq-decl nil vectors "vectors/")
    (n formal-const-decl "posnat" limit_vect_real nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (< const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers 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)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (eps skolem-const-decl
     "{n: nonneg_real | n >= l1!1 - l2!1 AND n >= -(l1!1 - l2!1)}"
     limit_vect_real nil)
    (l2!1 skolem-const-decl "real" limit_vect_real nil)
    (l1!1 skolem-const-decl "real" limit_vect_real nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (> const-decl "bool" reals nil)
    (nnreal_div_posreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (>= const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields 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)
    (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)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (convergence const-decl "bool" limit_vect_real nil))
   nil)
  (cv_unique-1 nil 3299406886
   ("" (grind :exclude ("abs" "norm" "-") :if-match nil)
    (("" (rewrite "abs_diff_0")
      (("" (name "eps" "abs(l1!1 - l2!1)")
        (("" (replace -1)
          (("" (inst -4 "eps/2")
            (("1" (inst -5 "eps/2")
              (("1" (assert)
                (("1" (skosimp*)
                  (("1"
                    (case " EXISTS (x: Vector): a!1 /= x AND norm(x - a!1) < delta!1 AND norm(x - a!1) < delta!2")
                    (("1" (skosimp*)
                      (("1" (inst?)
                        (("1" (inst?)
                          (("1" (assert)
                            (("1" (case "0 < norm(x!1 - a!1)")
                              (("1"
                                (assert)
                                (("1"
                                  (lemma "triangle2")
                                  (("1"
                                    (inst
                                     -
                                     "eps/2"
                                     "eps/2"
                                     "l1!1"
                                     "f!1(x!1)"
                                     "l2!1")
                                    (("1" (assertnil nil))
                                    nil))
                                  nil))
                                nil)
                               ("2"
                                (lemma "norm_eq_0")
                                (("2"
                                  (inst?)
                                  (("2"
                                    (assert)
                                    (("2"
                                      (replace -1 * lr)
                                      (("2"
                                        (assert)
                                        (("2"
                                          (rewrite "sub_eq_zero")
                                          nil
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (hide -4 -5)
                      (("2" (name "DEL" "min(delta!1,delta!2)")
                        (("2"
                          (name AA "a!1 WITH [0 := a!1(0) + DEL/2]")
                          (("1" (inst + "AA")
                            (("1" (case "norm(AA - a!1) = abs(DEL/2)")
                              (("1"
                                (replace -1 * lr)
                                (("1"
                                  (hide -1)
                                  (("1"
                                    (case "a!1 /= AA")
                                    (("1"
                                      (assert)
                                      (("1"
                                        (hide -1 -2)
                                        (("1" (grind) nil nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (flatten)
                                      (("2"
                                        (assert)
                                        (("2"
                                          (hide 1 -3 -4)
                                          (("2"
                                            (replace -1 * lr)
                                            (("2"
                                              (hide -1)
                                              (("2"
                                                (case
                                                 "AA WITH [(0) := AA(0) + DEL / 2](0) = AA(0)")
                                                (("1"
                                                  (hide -2)
                                                  (("1"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (replace -1 * lr)
                                                  (("2"
                                                    (propax)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil)
                               ("2"
                                (hide -1)
                                (("2"
                                  (reveal -1)
                                  (("2"
                                    (hide 2)
                                    (("2"
                                      (replace -1 * rl)
                                      (("2"
                                        (hide -1)
                                        (("2"
                                          (expand "norm")
                                          (("2"
                                            (case-replace
                                             "a!1 WITH [(0) := a!1(0) + DEL / 2] - a!1 =
             (LAMBDA (i: Index): IF i = 0 THEN DEL/2 ELSE 0 ENDIF)")
                                            (("1"
                                              (hide -1)
                                              (("1"
                                                (expand "sqv")
                                                (("1"
                                                  (expand "*")
                                                  (("1"
                                                    (lemma
                                                     "sigma_first")
                                                    (("1"
                                                      (inst?)
                                                      (("1"
                                                        (postpone)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("2" (postpone) nil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (postpone) nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (assertnil nil))
              nil)
             ("2" (assertnil nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((abs_diff_0 formula-decl nil abs_lems "reals/")
    (sqrt_square formula-decl nil sqrt "reals/")
    (triangle2 formula-decl nil abs_lems "reals/"))
   nil))
 (cv_in_domain 0
  (cv_in_domain-1 nil 3299406886
   ("" (grind :exclude ("abs" "norm" "-") :if-match nil)
    (("" (rewrite "abs_diff_0")
      (("" (inst - "abs(l!1 - f!1(x!1))")
        (("1" (skosimp*)
          (("1" (inst?)
            (("1" (assert)
              (("1" (rewrite "abs_diff_commute" -)
                (("1" (assertnil nil)) nil))
              nil))
            nil))
          nil)
         ("2" (assertnil nil))
        nil))
      nil))
    nil)
   ((abs_diff_0 formula-decl nil abs_lems "reals/")
    (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)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (n formal-const-decl "posnat" limit_vect_real nil)
    (Index type-eq-decl nil vectors "vectors/")
    (Vector type-eq-decl nil vectors "vectors/")
    (real_ge_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)
    (sub_eq_args formula-decl nil vectors "vectors/")
    (norm_zero formula-decl nil vectors "vectors/")
    (abs_diff_commute formula-decl nil abs_lems "reals/")
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_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)
    (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)
    (real nonempty-type-from-decl nil reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (convergence const-decl "bool" limit_vect_real nil))
   nil))
 (cv_sum 0
  (cv_sum-1 nil 3299406886
   ("" (grind :exclude ("abs" "norm" "-") :if-match nil)
    (("" (inst - "epsilon!1/2")
      (("" (inst - "epsilon!1/2")
        (("" (skosimp*)
          (("" (inst 1 "min(delta!1, delta!2)")
            (("" (skosimp*)
              (("" (inst?)
                (("" (inst?)
                  (("" (assert)
                    ((""
                      (lemma "triangle"
                       ("x" "f1!1(x!1) - l1!1" "y" "f2!1(x!1) - l2!1"))
                      (("" (assertnil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (triangle formula-decl nil real_props nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (Index type-eq-decl nil vectors "vectors/")
    (Vector type-eq-decl nil vectors "vectors/")
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (posreal_min application-judgement
     "{z: posreal | z <= x AND z <= y}" real_defs 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)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (+ const-decl "[Vector -> real]" vect_fun_ops "vectors/")
    (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)
    (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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (n formal-const-decl "posnat" limit_vect_real nil)
    (convergence const-decl "bool" limit_vect_real nil))
   nil))
 (cv_neg 0
  (cv_neg-1 nil 3299406886
   ("" (grind :exclude ("abs" "norm" "-") :if-match nil)
    (("" (inst - "epsilon!1")
      (("" (skolem!)
        (("" (inst + "delta!1")
          (("" (skosimp)
            (("" (inst?)
              (("" (assert)
                (("" (expand "-")
                  (("" (lemma "abs_neg")
                    (("" (inst - "f!1(x!1) - l!1")
                      (("" (assertnil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((minus_odd_is_odd application-judgement "odd_int" integers 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (n formal-const-decl "posnat" limit_vect_real nil)
    (Index type-eq-decl nil vectors "vectors/")
    (Vector type-eq-decl nil vectors "vectors/")
    (- const-decl "[Vector -> real]" vect_fun_ops "vectors/")
    (- const-decl "real" vectors "vectors/")
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (abs_neg formula-decl nil abs_lems "reals/")
    (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)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props 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)
    (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)
    (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)
    (minus_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (convergence const-decl "bool" limit_vect_real nil))
   nil))
 (cv_diff 0
  (cv_diff-1 nil 3299406886
   ("" (skosimp*)
    (("" (rewrite "diff_function")
      (("" (lemma "cv_sum")
        (("" (inst?)
          (("" (inst - "(-f2!1)" "-l2!1")
            (("" (assert)
              (("" (hide 2)
                (("" (lemma "cv_neg")
                  (("" (inst?) (("" (assertnil nil)) nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((diff_function formula-decl nil vect_fun_ops "vectors/")
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (Index type-eq-decl nil vectors "vectors/")
    (Vector type-eq-decl nil vectors "vectors/")
    (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)
    (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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (n formal-const-decl "posnat" limit_vect_real nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (cv_neg formula-decl nil limit_vect_real nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[Vector -> real]" vect_fun_ops "vectors/")
    (minus_real_is_real application-judgement "real" reals nil)
    (cv_sum formula-decl nil limit_vect_real nil))
   nil))
 (cv_prod 0
  (cv_prod-2 nil 3442332189
   ("" (grind :exclude ("abs" "norm" "-") :if-match nil)
    ((""
      (lemma "prod_epsilon" ("y1" "l1!1" "y2" "l2!1" "e" "epsilon!1"))
      (("" (skosimp*)
        (("" (inst - "e1!1")
          (("" (inst - "e2!1")
            (("" (skosimp*)
              (("" (inst 1 "min(delta!1, delta!2)")
                (("" (skosimp*)
                  (("" (inst?)
                    (("" (inst?)
                      (("" (assert)
                        (("" (lemma "prod_bound")
                          ((""
                            (inst -1 "e1!1" "e2!1" "f1!1(x!1)"
                             "f2!1(x!1)" "l1!1" "l2!1")
                            (("" (assertnil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((prod_epsilon formula-decl nil epsilon_lemmas "analysis/")
    (prod_bound formula-decl nil epsilon_lemmas "analysis/")
    (nnreal_plus_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posreal_plus_nnreal_is_posreal application-judgement "posreal"
     real_types nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (Index type-eq-decl nil vectors "vectors/")
    (Vector type-eq-decl nil vectors "vectors/")
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (posreal_min application-judgement
     "{z: posreal | z <= x AND z <= y}" real_defs 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)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (* const-decl "[Vector -> real]" vect_fun_ops "vectors/")
    (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)
    (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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (n formal-const-decl "posnat" limit_vect_real nil)
    (convergence const-decl "bool" limit_vect_real nil))
   nil)
  (cv_prod-1 nil 3299406886
   ("" (grind :exclude ("abs" "norm" "-") :if-match nil)
    ((""
      (lemma "prod_epsilon"
       ("y1" "l1!1" "y2" "l2!1" "epsilon" "epsilon!1"))
      (("" (skosimp*)
        (("" (inst - "e1!1")
          (("" (inst - "e2!1")
            (("" (skosimp*)
              (("" (inst 1 "min(delta!1, delta!2)")
                (("" (skosimp*)
                  (("" (inst?)
                    (("" (inst?)
                      (("" (assert) (("" (postpone) nil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   nil nil))
 (cv_const 0
  (cv_const-1 nil 3299406886
   ("" (expand "convergence")
    (("" (skosimp*)
      (("" (expand "const_fun") (("" (assertnil nil)) nil)) nil))
    nil)
   ((abs_0 formula-decl nil abs_lems "reals/")
    (const_fun const-decl "[Vector -> real]" vect_fun_ops "vectors/")
    (convergence const-decl "bool" limit_vect_real nil)
    (real_minus_real_is_real application-judgement "real" reals nil))
   nil))
 (cv_scal 0
  (cv_scal-1 nil 3299406886
   ("" (skosimp)
    (("" (rewrite "scal_function")
      (("" (rewrite "cv_prod")
        (("" (hide 2) (("" (rewrite "cv_const"nil nil)) nil)) nil))
      nil))
    nil)
   ((scal_function formula-decl nil vect_fun_ops "vectors/")
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (Index type-eq-decl nil vectors "vectors/")
    (Vector type-eq-decl nil vectors "vectors/")
    (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)
    (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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (n formal-const-decl "posnat" limit_vect_real nil)
    (cv_const formula-decl nil limit_vect_real nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (const_fun const-decl "[Vector -> real]" vect_fun_ops "vectors/")
    (cv_prod formula-decl nil limit_vect_real nil))
   nil))
 (cv_inv 0
  (cv_inv-2 nil 3442332397
   ("" (grind :exclude ("abs" "norm" "-") :if-match nil)
    (("" (lemma "inv_epsilon" ("y1" "l!1" "e" "epsilon!1"))
      (("" (assert)
        (("" (skosimp)
          (("" (inst? -)
            (("" (skosimp*)
              (("" (inst + "delta!1")
                (("" (skosimp*)
                  (("" (inst?)
                    (("" (assert)
                      ((""
                        (lemma "inv_bound"
                         ("e1" "e1!1" "x1" "g!1(x!1)" "y1" "l!1"))
                        (("" (assertnil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((inv_epsilon formula-decl nil epsilon_lemmas "analysis/")
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nzreal nonempty-type-eq-decl nil reals nil)
    (inv_bound formula-decl nil epsilon_lemmas "analysis/")
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (Index type-eq-decl nil vectors "vectors/")
    (Vector type-eq-decl nil vectors "vectors/")
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types 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)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (/ const-decl "[Vector -> real]" vect_fun_ops "vectors/")
    (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)
    (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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (n formal-const-decl "posnat" limit_vect_real nil)
    (/= const-decl "boolean" notequal nil)
    (convergence const-decl "bool" limit_vect_real nil))
   nil)
  (cv_inv-1 nil 3299406886
   ("" (expand "convergence")
    (("" (grind :defs nil :rewrites "convergence_inv[T]"nil nil))
    nil)
   nil nil))
 (cv_div 0
  (cv_div-1 nil 3299406886
   ("" (skosimp*)
    (("" (rewrite "div_function")
      (("" (assert)
        (("" (use "cv_prod" ("l2" "1/l2!1"))
          (("" (assert) (("" (rewrite "cv_inv"nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((div_function formula-decl nil vect_fun_ops "vectors/")
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (Index type-eq-decl nil vectors "vectors/")
    (Vector type-eq-decl nil vectors "vectors/")
    (/= const-decl "boolean" notequal nil)
    (nzreal nonempty-type-eq-decl nil reals nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (n formal-const-decl "posnat" limit_vect_real nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (cv_prod formula-decl nil limit_vect_real nil)
    (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (/ const-decl "[Vector -> real]" vect_fun_ops "vectors/")
    (cv_inv formula-decl nil limit_vect_real nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil))
   nil))
 (lim_fun_lemma 0
  (lim_fun_lemma-2 nil 3444672843
   ("" (skolem!)
    (("" (name-replace "ll" "lim(f!1, x0!1)" :hide? nil)
      (("" (expand "lim" -)
        ((""
          (lemma "epsilon_ax"
           ("p" "LAMBDA (l: real): convergence(f!1, x0!1, l)"))
          (("" (assert)
            (("" (typepred "x0!1")
              (("" (expand "convergent?") (("" (propax) nil nil)) 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)
    (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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (n formal-const-decl "posnat" limit_vect_real nil)
    (Index type-eq-decl nil vectors "vectors/")
    (Vector type-eq-decl nil vectors "vectors/")
    (convergent? const-decl "bool" limit_vect_real nil)
    (lim const-decl "real" limit_vect_real nil)
    (convergence const-decl "bool" limit_vect_real nil)
    (pred type-eq-decl nil defined_types nil)
    (epsilon_ax formula-decl nil epsilons nil)
    (NOT const-decl "[bool -> bool]" booleans nil))
   nil)
  (lim_fun_lemma-1 nil 3299406886
   ("" (skolem!)
    (("" (name-replace "ll" "lim(f!1, x0!1)" :hide? nil)
      (("" (expand "lim" -)
        ((""
          (lemma "epsilon_ax"
           ("p" "LAMBDA (l: real): convergence(f!1, x0!1, l)"))
          (("" (assert)
            (("" (typepred "x0!1")
              (("" (expand "convergent") (("" (propax) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((Index type-eq-decl nil vectors "vectors/")
    (Vector type-eq-decl nil vectors "vectors/"))
   nil))
 (lim_fun_def 0
  (lim_fun_def-1 nil 3299406886
   ("" (skolem!)
    (("" (use "lim_fun_lemma")
      (("" (ground)
        (("" (use "cv_unique" ("l2" "lim(f!1, x0!1)"))
          (("" (assertnil nil)) nil))
        nil))
      nil))
    nil)
   ((lim_fun_lemma formula-decl nil limit_vect_real nil)
    (convergent? const-decl "bool" limit_vect_real nil)
    (Vector type-eq-decl nil vectors "vectors/")
    (Index type-eq-decl nil vectors "vectors/")
    (n formal-const-decl "posnat" limit_vect_real nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (< const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (cv_unique formula-decl nil limit_vect_real nil)
    (lim const-decl "real" limit_vect_real nil))
   nil))
 (convergence_equiv 0
  (convergence_equiv-1 nil 3299406886
   ("" (skolem!)
    (("" (prop)
      (("1" (expand "convergent?") (("1" (inst?) nil nil)) nil)
       ("2" (rewrite "lim_fun_def")
        (("2" (expand "convergent?") (("2" (inst?) nil nil)) nil)) nil)
       ("3" (rewrite "lim_fun_def"nil nil))
      nil))
    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)
    (convergent? const-decl "bool" limit_vect_real nil)
    (Vector type-eq-decl nil vectors "vectors/")
    (Index type-eq-decl nil vectors "vectors/")
    (n formal-const-decl "posnat" limit_vect_real nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (< const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans 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)
    (lim_fun_def formula-decl nil limit_vect_real nil))
   nil))
 (convergent_in_domain 0
  (convergent_in_domain-1 nil 3299406886
   ("" (grind :exclude "convergence")
    (("" (forward-chain "cv_in_domain") (("" (assertnil nil)) nil))
    nil)
   ((cv_in_domain formula-decl nil limit_vect_real nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (Vector type-eq-decl nil vectors "vectors/")
    (Index type-eq-decl nil vectors "vectors/")
    (n formal-const-decl "posnat" limit_vect_real nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (< const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (convergent? const-decl "bool" limit_vect_real nil))
   nil))
 (lim_in_domain 0
  (lim_in_domain-1 nil 3299406886
   ("" (skosimp)
    (("" (rewrite "lim_fun_def")
      (("" (rewrite "convergent_in_domain"nil nil)) nil))
    nil)
   ((lim_fun_def formula-decl nil limit_vect_real 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)
    (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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (n formal-const-decl "posnat" limit_vect_real nil)
    (Index type-eq-decl nil vectors "vectors/")
    (Vector type-eq-decl nil vectors "vectors/")
    (convergent? const-decl "bool" limit_vect_real nil)
    (convergent_in_domain formula-decl nil limit_vect_real nil))
   nil))
 (sum_fun_convergent 0
  (sum_fun_convergent-1 nil 3299406886
   ("" (expand "convergent?")
    (("" (skosimp*)
      (("" (inst 1 "l!1 + l!2") (("" (rewrite "cv_sum"nil nil)) nil))
      nil))
    nil)
   ((cv_sum formula-decl nil limit_vect_real 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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (n formal-const-decl "posnat" limit_vect_real nil)
    (Index type-eq-decl nil vectors "vectors/")
    (Vector type-eq-decl nil vectors "vectors/")
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields 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)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (convergent? const-decl "bool" limit_vect_real nil))
   nil))
 (neg_fun_convergent 0
  (neg_fun_convergent-1 nil 3299406886
   ("" (expand "convergent?")
    (("" (skosimp*)
      (("" (forward-chain "cv_neg") (("" (inst?) nil nil)) nil)) nil))
    nil)
   ((numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (Vector type-eq-decl nil vectors "vectors/")
    (Index type-eq-decl nil vectors "vectors/")
    (n formal-const-decl "posnat" limit_vect_real nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (< const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (cv_neg formula-decl nil limit_vect_real nil)
    (convergent? const-decl "bool" limit_vect_real nil))
   nil))
 (diff_fun_convergent 0
  (diff_fun_convergent-1 nil 3299406886
   ("" (expand "convergent?")
    (("" (skosimp*)
      (("" (inst 1 "l!1 - l!2") (("" (rewrite "cv_diff"nil nil))
        nil))
      nil))
    nil)
   ((cv_diff formula-decl nil limit_vect_real nil)
--> --------------------

--> maximum size reached

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

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