(topological_convergence
 (limit_TCC1 0
  (limit_TCC1-1 nil 3454592307 ("" (existence-tcc) nil 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)
    (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)
    (T formal-type-decl nil topological_convergence nil)
    (sequence type-eq-decl nil sequences nil)
    (convergent? const-decl "bool" topological_convergence nil)
    (convergent type-eq-decl nil topological_convergence nil)
    (convergence? const-decl "bool" topological_convergence nil))
   nil))
 (limit_lemma 0
  (limit_lemma-1 nil 3358827431
   ("" (skosimp)
    (("" (typepred "v!1")
      (("" (expand "convergent?")
        (("" (skosimp)
          (("" (expand "limit")
            ((""
              (lemma "epsilon_ax"
               ("p" "LAMBDA l: convergence?(v!1,l)"))
              (("" (split -1)
                (("1" (assert) nil nil) ("2" (inst + "l!1") nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((convergent type-eq-decl nil topological_convergence nil)
    (convergent? const-decl "bool" topological_convergence nil)
    (sequence type-eq-decl nil sequences nil)
    (T formal-type-decl nil topological_convergence nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals 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)
    (number nonempty-type-decl nil numbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (convergence? const-decl "bool" topological_convergence nil)
    (pred type-eq-decl nil defined_types nil)
    (epsilon_ax formula-decl nil epsilons nil)
    (limit const-decl "T" topological_convergence nil))
   shostak))
 (limit_accumulation 0
  (limit_accumulation-1 nil 3358827716
   ("" (skosimp)
    (("" (expand "accumulation?")
      (("" (expand "convergence?")
        (("" (skosimp*)
          (("" (inst - "U!1")
            (("" (assert)
              (("" (skosimp)
                (("" (inst + "max(n!1,n!2)")
                  (("" (inst - "max(n!1,n!2)")
                    (("" (expand "max") (("" (grind) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((accumulation? const-decl "bool" topological_convergence nil)
    (nonneg_rat_max application-judgement
     "{s: nonneg_rat | s >= q AND s >= r}" real_defs nil)
    (nat_max application-judgement "{k: nat | i <= k AND j <= k}"
     real_defs 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)
    (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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
    (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)
    (open nonempty-type-eq-decl nil topology nil)
    (open? const-decl "bool" topology nil)
    (S formal-const-decl "topology[T]" topological_convergence nil)
    (topology nonempty-type-eq-decl nil topology_prelim nil)
    (topology? const-decl "bool" topology_prelim nil)
    (setofsets type-eq-decl nil sets nil)
    (setof type-eq-decl nil defined_types nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-type-decl nil topological_convergence nil)
    (convergence? const-decl "bool" topological_convergence nil))
   shostak))
 (convergence_subsequence 0
  (convergence_subsequence-1 nil 3358829042
   ("" (skosimp)
    (("" (expand "subseq?")
      (("" (expand "convergence?")
        (("" (skosimp*)
          (("" (inst - "U!1")
            (("" (assert)
              (("" (skosimp)
                (("" (inst + "n!1")
                  (("" (skosimp)
                    (("" (inst - "f!1(i!1)")
                      (("" (inst - "i!1")
                        (("" (replace -2)
                          (("" (split -1)
                            (("1" (propax) nil nil)
                             ("2" (hide -1 -2 2)
                              (("2"
                                (case "forall n: n <= f!1(n)")
                                (("1"
                                  (inst - "i!1")
                                  (("1" (assert) nil nil))
                                  nil)
                                 ("2"
                                  (hide-all-but 1)
                                  (("2"
                                    (induct "n")
                                    (("1" (assert) nil nil)
                                     ("2"
                                      (skosimp*)
                                      (("2"
                                        (typepred "f!1")
                                        (("2"
                                          (expand "strict_increasing?")
                                          (("2"
                                            (inst - "j!1" "j!1+1")
                                            (("2" (assert) nil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((subseq? const-decl "bool" subseq 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)
    (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)
    (strict_increasing? const-decl "bool" real_fun_preds "reals/")
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (pred type-eq-decl nil defined_types nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (<= const-decl "bool" reals nil)
    (open nonempty-type-eq-decl nil topology nil)
    (open? const-decl "bool" topology nil)
    (S formal-const-decl "topology[T]" topological_convergence nil)
    (topology nonempty-type-eq-decl nil topology_prelim nil)
    (topology? const-decl "bool" topology_prelim nil)
    (setofsets type-eq-decl nil sets nil)
    (setof type-eq-decl nil defined_types nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-type-decl nil topological_convergence nil)
    (convergence? const-decl "bool" topological_convergence nil))
   shostak)))

