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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: dml034.mco   Sprache: Unknown

Original von: PVS©

(sup_norm
 (bounded_TCC1 0
  (bounded_TCC1-1 nil 3392430087
   ("" (expand "bounded?")
    (("" (inst + "0") (("" (grind) 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)
    (nnreal type-eq-decl nil real_types nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (bounded? const-decl "bool" sup_norm nil))
   nil))
 (bounded_add 0
  (bounded_add-1 nil 3392432560
   ("" (skosimp)
    (("" (typepred "f1!1")
      (("" (typepred "f2!1")
        (("" (expand "+")
          (("" (expand "bounded?")
            (("" (skosimp*)
              (("" (inst + "c!1+c!2")
                (("" (skosimp)
                  (("" (inst - "x!1")
                    (("" (inst - "x!1") (("" (grind) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((bounded nonempty-type-eq-decl nil sup_norm nil)
    (bounded? const-decl "bool" sup_norm 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)
    (T formal-type-decl nil sup_norm nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (+ const-decl "[T -> real]" real_fun_ops "reals/")
    (minus_real_is_real application-judgement "real" reals nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (>= const-decl "bool" reals nil)
    (nnreal type-eq-decl nil real_types nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil))
   nil))
 (bounded_scal 0
  (bounded_scal-1 nil 3392432560
   ("" (skosimp)
    (("" (expand "*")
      (("" (typepred "f!1")
        (("" (expand "bounded?")
          (("" (skosimp)
            (("" (inst + " abs(y!1)*c!1")
              (("" (skosimp)
                (("" (inst - "x!1")
                  (("" (rewrite "abs_mult")
                    (("" (typepred "abs(y!1)")
                      (("" (hide -2 -3)
                        (("" (expand ">=")
                          (("" (expand "<=" -1)
                            (("" (split -1)
                              (("1"
                                (lemma
                                 "both_sides_times_pos_le1"
                                 ("pz"
                                  "abs(y!1)"
                                  "x"
                                  "abs(f!1(x!1))"
                                  "y"
                                  "c!1"))
                                (("1" (assertnil nil)
                                 ("2" (assertnil nil))
                                nil)
                               ("2"
                                (replace -1 * rl)
                                (("2" (assertnil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_times_real_is_real application-judgement "real" reals nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (>= const-decl "bool" reals nil)
    (nnreal type-eq-decl nil real_types nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (both_sides_times_pos_le1 formula-decl nil real_props nil)
    (<= const-decl "bool" reals nil)
    (abs_mult formula-decl nil 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)
    (T formal-type-decl nil sup_norm 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)
    (bounded? const-decl "bool" sup_norm nil)
    (bounded nonempty-type-eq-decl nil sup_norm nil))
   nil))
 (bounded_opp 0
  (bounded_opp-1 nil 3392432840
   ("" (skosimp)
    (("" (lemma "bounded_scal" ("y" "-1" "f" "f!1"))
      (("" (expand "*") (("" (expand "-") (("" (assertnil nil)) nil))
        nil))
      nil))
    nil)
   ((- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (bounded nonempty-type-eq-decl nil sup_norm nil)
    (bounded? const-decl "bool" sup_norm 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)
    (T formal-type-decl nil sup_norm nil)
    (bounded_scal judgement-tcc nil sup_norm nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (- const-decl "[T -> real]" real_fun_ops "reals/")
    (real_times_real_is_real application-judgement "real" reals nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/"))
   nil))
 (bounded_diff 0
  (bounded_diff-1 nil 3392432560
   ("" (skosimp)
    (("" (typepred "f2!1")
      (("" (lemma "bounded_opp" ("f" "f2!1"))
        (("" (lemma "bounded_add" ("f1" "f1!1" "f2" "-f2!1"))
          (("" (expand "+")
            (("" (expand "-") (("" (assertnil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((bounded nonempty-type-eq-decl nil sup_norm nil)
    (bounded? const-decl "bool" sup_norm 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)
    (T formal-type-decl nil sup_norm nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bounded_opp application-judgement "bounded" sup_norm nil)
    (bounded_add judgement-tcc nil sup_norm nil)
    (- const-decl "[T -> real]" real_fun_ops "reals/")
    (real_minus_real_is_real application-judgement "real" reals nil)
    (- const-decl "[T -> real]" real_fun_ops "reals/")
    (real_plus_real_is_real application-judgement "real" reals nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (+ const-decl "[T -> real]" real_fun_ops "reals/")
    (bounded_opp judgement-tcc nil sup_norm nil))
   nil))
 (sup_norm_TCC1 0
  (sup_norm_TCC1-1 nil 3392429651
   ("" (skosimp*)
    (("" (split)
      (("1" (expand "extend")
        (("1" (expand "nonempty?")
          (("1" (expand "empty?")
            (("1" (expand "member")
              (("1" (inst - "abs(f!1(x!1))")
                (("1" (assert)
                  (("1" (prop)
                    (("1" (inst + "x!1"nil nil)
                     ("2" (assertnil nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (typepred "f!1")
        (("2" (expand "bounded?")
          (("2" (skosimp)
            (("2" (expand "extend")
              (("2" (expand "above_bounded")
                (("2" (inst + "c!1")
                  (("2" (expand "upper_bound")
                    (("2" (skosimp)
                      (("2" (typepred "z!1")
                        (("2" (assert)
                          (("2" (skosimp)
                            (("2" (inst - "x!2")
                              (("2" (assertnil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((nonempty? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (bounded nonempty-type-eq-decl nil sup_norm nil)
    (bounded? const-decl "bool" sup_norm nil)
    (T formal-type-decl nil sup_norm 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)
    (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)
    (empty? const-decl "bool" sets nil)
    (extend const-decl "R" extend nil)
    (nnreal type-eq-decl nil real_types nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (FALSE const-decl "bool" booleans nil)
    (upper_bound const-decl "bool" bound_defs "reals/")
    (above_bounded const-decl "bool" bounded_reals "reals/")
    (NOT const-decl "[bool -> bool]" booleans nil))
   nil))
 (sup_norm_TCC2 0
  (sup_norm_TCC2-1 nil 3392429651
   ("" (skosimp*)
    (("" (expand "extend")
      ((""
        (typepred "sup[real]
          (LAMBDA (t: real):
             IF t >= 0 THEN EXISTS x: abs(f!1(x)) = t ELSE FALSE ENDIF)")
        (("1"
          (name-replace "SUP" "sup[real]
          (LAMBDA (t: real):
             IF t >= 0 THEN EXISTS x: abs(f!1(x)) = t ELSE FALSE ENDIF)")
          (("1" (expand "least_upper_bound")
            (("1" (flatten)
              (("1" (expand "upper_bound")
                (("1" (inst - "abs(f!1(x!1))")
                  (("1" (assertnil nil)
                   ("2" (prop)
                    (("1" (inst + "x!1"nil nil)
                     ("2" (assertnil nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (lemma "sup_norm_TCC1" ("f" "f!1"))
          (("2" (split -1)
            (("1" (expand "extend") (("1" (propax) nil nil)) nil)
             ("2" (inst + "x!1"nil nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((extend const-decl "R" extend nil)
    (sup_norm_TCC1 subtype-tcc nil sup_norm nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (f!1 skolem-const-decl "bounded" sup_norm nil)
    (x!1 skolem-const-decl "T" sup_norm nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (upper_bound const-decl "bool" bound_defs "reals/")
    (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)
    (pred type-eq-decl nil defined_types nil)
    (least_upper_bound const-decl "bool" bound_defs "reals/")
    (<= const-decl "bool" reals nil) (set type-eq-decl nil sets nil)
    (nonempty? const-decl "bool" sets nil)
    (setof type-eq-decl nil defined_types nil)
    (above_bounded const-decl "bool" bounded_reals "reals/")
    (sup_set type-eq-decl nil bounded_reals "reals/")
    (sup const-decl "{x | least_upper_bound(<=)(x, Su)}" bounded_reals
     "reals/")
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (>= const-decl "bool" reals nil)
    (T formal-type-decl nil sup_norm nil)
    (= const-decl "[T, T -> boolean]" equalities 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)
    (bounded? const-decl "bool" sup_norm nil)
    (bounded nonempty-type-eq-decl nil sup_norm nil)
    (FALSE const-decl "bool" booleans nil))
   nil))
 (sup_norm_eq_0 0
  (sup_norm_eq_0-1 nil 3392433034
   ("" (skosimp)
    ((""
      (lemma "extensionality_postulate"
       ("f" "f!1" "g" "const_fun[T, real](0)"))
      (("" (replace -1 1 rl)
        (("" (hide -1)
          (("" (expand "const_fun")
            (("" (expand "sup_norm")
              (("" (case-replace "EXISTS x: TRUE")
                (("1"
                  (typepred "sup(extend[real, nnreal, bool, FALSE]
              ({c | EXISTS (x_1: T): abs(f!1(x_1)) = c}))")
                  (("1"
                    (name-replace "SUP"
                     "sup(extend[real, nnreal, bool, FALSE]
              ({c | EXISTS (x_1: T): abs(f!1(x_1)) = c}))")
                    (("1" (expand "least_upper_bound")
                      (("1" (flatten)
                        (("1" (expand "extend")
                          (("1" (expand "upper_bound")
                            (("1" (split 1)
                              (("1"
                                (flatten)
                                (("1"
                                  (replace -1)
                                  (("1"
                                    (skosimp)
                                    (("1"
                                      (typepred "abs(f!1(x!1))")
                                      (("1"
                                        (hide -2 -3)
                                        (("1"
                                          (inst -3 "abs(f!1(x!1))")
                                          (("1"
                                            (hide-all-but (-1 -3 1))
                                            (("1" (grind) nil nil))
                                            nil)
                                           ("2"
                                            (assert)
                                            (("2"
                                              (inst + "x!1")
                                              nil
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil)
                               ("2"
                                (flatten)
                                (("2"
                                  (skosimp)
                                  (("2"
                                    (inst-cp - "x!1")
                                    (("2"
                                      (inst -3 "0")
                                      (("1"
                                        (inst -4 "0")
                                        (("1"
                                          (split -4)
                                          (("1" (assertnil nil)
                                           ("2" (propax) nil nil)
                                           ("3"
                                            (skosimp)
                                            (("3"
                                              (typepred "z!1")
                                              (("3"
                                                (assert)
                                                (("3"
                                                  (skosimp)
                                                  (("3"
                                                    (inst - "x!2")
                                                    (("3"
                                                      (replace -3)
                                                      (("3"
                                                        (expand "abs")
                                                        (("3"
                                                          (assert)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil)
                                       ("2"
                                        (inst + "x!1")
                                        (("2"
                                          (replace -2)
                                          (("2"
                                            (expand "abs")
                                            (("2" (propax) nil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (replace 1 2)
                  (("2" (assert)
                    (("2" (skosimp) (("2" (inst + "x!1"nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          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)
    (T formal-type-decl nil sup_norm nil)
    (const_fun const-decl "[S -> T]" const_fun_def "structures/")
    (bounded nonempty-type-eq-decl nil sup_norm nil)
    (bounded? const-decl "bool" sup_norm nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (extensionality_postulate formula-decl nil functions nil)
    (sup_norm const-decl "nnreal" sup_norm 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)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (extend const-decl "R" extend nil)
    (FALSE const-decl "bool" booleans nil)
    (nnreal type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (sup const-decl "{x | least_upper_bound(<=)(x, Su)}" bounded_reals
     "reals/")
    (sup_set type-eq-decl nil bounded_reals "reals/")
    (above_bounded const-decl "bool" bounded_reals "reals/")
    (setof type-eq-decl nil defined_types nil)
    (nonempty? const-decl "bool" sets nil)
    (set type-eq-decl nil sets nil) (<= const-decl "bool" reals nil)
    (least_upper_bound const-decl "bool" bound_defs "reals/")
    (pred type-eq-decl nil defined_types nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (f!1 skolem-const-decl "bounded" sup_norm nil)
    (x!1 skolem-const-decl "T" sup_norm nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (upper_bound const-decl "bool" bound_defs "reals/")
    (TRUE const-decl "bool" booleans nil))
   shostak))
 (sup_norm_neg 0
  (sup_norm_neg-1 nil 3392433144
   ("" (skosimp)
    (("" (expand "sup_norm")
      (("" (case-replace "EXISTS x: TRUE")
        (("1"
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          (("1"
            (name-replace "SUP" "sup(extend[real, nnreal, bool, FALSE]
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            (("1"
              (typepred "sup(extend[real, nnreal, bool, FALSE]
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              (("1"
                (name-replace "SUPN"
                 "sup(extend[real, nnreal, bool, FALSE]
              ({c_1: nnreal | EXISTS (x_2: T): abs((-f!1)(x_2)) = c_1}))")
                (("1" (expand "extend")
                  (("1" (expand "least_upper_bound")
                    (("1" (flatten)
                      (("1" (inst -2 "SUP")
                        (("1" (split -2)
                          (("1" (inst -4 "SUPN")
                            (("1" (split -4)
                              (("1" (assertnil nil)
                               ("2" (assertnil nil)
                               ("3"
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                                (("3"
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                                  (("3"
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                                    (("3"
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                                      (("3"
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                                          (skosimp)
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                                            (("3"
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                                              (("3"
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                                                (("3" (grind) nil nil))
                                                nil))
                                              nil))
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                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (propax) nil nil)
                           ("3" (expand "upper_bound")
                            (("3" (skosimp)
                              (("3"
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                                (("3"
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                                      (("3"
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                                        (("3"
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                                          nil))
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                                    nil))
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                                nil))
                              nil))
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                          nil))
                        nil))
                      nil))
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                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (replace 1 2) (("2" (propax) nil nil)) nil))
        nil))
      nil))
    nil)
   ((sup_norm const-decl "nnreal" sup_norm nil)
    (bounded nonempty-type-eq-decl nil sup_norm nil)
    (bounded? const-decl "bool" sup_norm 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)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (extend const-decl "R" extend nil)
    (FALSE const-decl "bool" booleans nil)
    (nnreal type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (sup const-decl "{x | least_upper_bound(<=)(x, Su)}" bounded_reals
     "reals/")
    (sup_set type-eq-decl nil bounded_reals "reals/")
    (above_bounded const-decl "bool" bounded_reals "reals/")
    (setof type-eq-decl nil defined_types nil)
    (nonempty? const-decl "bool" sets nil)
    (set type-eq-decl nil sets nil) (<= const-decl "bool" reals nil)
    (least_upper_bound const-decl "bool" bound_defs "reals/")
    (pred type-eq-decl nil defined_types 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)
    (- const-decl "[T -> real]" real_fun_ops "reals/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (upper_bound const-decl "bool" bound_defs "reals/")
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (bounded_opp application-judgement "bounded" sup_norm nil)
    (z!1 skolem-const-decl
     "{t | IF t >= 0 THEN EXISTS (x_1: T): abs(f!1(x_1)) = t ELSE FALSE ENDIF}"
     sup_norm nil)
    (f!1 skolem-const-decl "bounded" sup_norm nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (z!1 skolem-const-decl
     "{t | IF t >= 0 THEN EXISTS (x_2: T): abs((-f!1)(x_2)) = t ELSE FALSE ENDIF}"
     sup_norm nil)
    (TRUE const-decl "bool" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-type-decl nil sup_norm nil))
   shostak))
 (sup_norm_sum 0
  (sup_norm_sum-1 nil 3392434044
   ("" (skosimp)
    (("" (expand "sup_norm")
      (("" (case-replace "EXISTS x: TRUE")
        (("1"
          (typepred "sup(extend[real, nnreal, bool, FALSE]
                ({c | EXISTS (x_1: T): abs(f2!1(x_1)) = c}))")
          (("1"
            (name-replace "SUP2" "sup(extend[real, nnreal, bool, FALSE]
                ({c | EXISTS (x_1: T): abs(f2!1(x_1)) = c}))")
            (("1"
              (typepred "sup(extend[real, nnreal, bool, FALSE]
               ({c_1: nnreal | EXISTS (x_2: T): abs(f1!1(x_2)) = c_1}))")
              (("1"
                (name-replace "SUP1"
                 "sup(extend[real, nnreal, bool, FALSE]
               ({c_1: nnreal | EXISTS (x_2: T): abs(f1!1(x_2)) = c_1}))")
                (("1"
                  (typepred "sup(extend[real, nnreal, bool, FALSE]
              ({c_2: nnreal |
                  EXISTS (x_1: T): abs((f1!1 + f2!1)(x_1)) = c_2}))")
                  (("1"
                    (name-replace "SUP"
                     "sup(extend[real, nnreal, bool, FALSE]
              ({c_2: nnreal |
                  EXISTS (x_1: T): abs((f1!1 + f2!1)(x_1)) = c_2}))")
                    (("1" (expand "extend")
                      (("1" (expand "least_upper_bound")
                        (("1" (flatten)
                          (("1" (hide -4 -6)
                            (("1" (inst -2 "SUP1 + SUP2")
                              (("1"
                                (split -2)
                                (("1" (propax) nil nil)
                                 ("2" (assertnil nil)
                                 ("3"
                                  (hide 2)
                                  (("3"
                                    (expand "upper_bound")
                                    (("3"
                                      (skosimp)
                                      (("3"
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                                        (("3"
                                          (assert)
                                          (("3"
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                                            (("3"
                                              (expand "+" -1)
                                              (("3"
                                                (hide -3)
                                                (("3"
                                                  (inst
                                                   -
                                                   "abs(f1!1(x!1))")
                                                  (("1"
                                                    (inst
                                                     -
                                                     "abs(f2!1(x!1))")
                                                    (("1"
                                                      (grind)
                                                      nil
                                                      nil)
                                                     ("2"
                                                      (typepred
                                                       "abs(f2!1(x!1))")
                                                      (("2"
                                                        (assert)
                                                        (("2"
                                                          (inst
                                                           +
                                                           "x!1")
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil)
                                                   ("2"
                                                    (typepred
                                                     "abs(f1!1(x!1))")
                                                    (("2"
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                                                      (("2"
                                                        (inst + "x!1")
                                                        nil
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                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
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                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (replace 1 2) (("2" (assertnil nil)) nil))
        nil))
      nil))
    nil)
   ((sup_norm const-decl "nnreal" sup_norm nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (even_plus_even_is_even application-judgement "even_int" integers
     nil)
    (bounded nonempty-type-eq-decl nil sup_norm nil)
    (bounded? const-decl "bool" sup_norm 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)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (extend const-decl "R" extend nil)
    (FALSE const-decl "bool" booleans nil)
    (nnreal type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (sup const-decl "{x | least_upper_bound(<=)(x, Su)}" bounded_reals
     "reals/")
    (sup_set type-eq-decl nil bounded_reals "reals/")
    (above_bounded const-decl "bool" bounded_reals "reals/")
    (setof type-eq-decl nil defined_types nil)
    (nonempty? const-decl "bool" sets nil)
    (set type-eq-decl nil sets nil) (<= const-decl "bool" reals nil)
    (least_upper_bound const-decl "bool" bound_defs "reals/")
    (pred type-eq-decl nil defined_types 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)
    (+ const-decl "[T -> real]" real_fun_ops "reals/")
    (real_plus_real_is_real application-judgement "real" reals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (f1!1 skolem-const-decl "bounded" sup_norm nil)
    (x!1 skolem-const-decl "T" sup_norm nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (f2!1 skolem-const-decl "bounded" sup_norm nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (upper_bound const-decl "bool" bound_defs "reals/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (TRUE const-decl "bool" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-type-decl nil sup_norm nil))
   shostak))
 (sup_norm_prop 0
  (sup_norm_prop-1 nil 3394593866
   ("" (skosimp*)
    (("" (typepred "sup_norm(f!1)")
      (("" (expand "sup_norm")
        (("" (case-replace "EXISTS x: TRUE")
          (("1" (expand "extend")
            (("1" (skolem - ("XX"))
              (("1"
                (typepred "sup(LAMBDA (t: real):
            IF t >= 0 THEN EXISTS (x_1: T): abs(f!1(x_1)) = t
            ELSE FALSE
            ENDIF)")
                (("1"
                  (name-replace "SUP" "sup(LAMBDA (t: real):
            IF t >= 0 THEN EXISTS (x_1: T): abs(f!1(x_1)) = t
            ELSE FALSE
            ENDIF)")
                  (("1" (expand "least_upper_bound")
                    (("1" (flatten)
                      (("1" (expand "upper_bound")
                        (("1" (split)
                          (("1" (skosimp)
                            (("1" (inst - "abs(f!1(x!1))")
                              (("1"
                                (assert)
                                (("1" (inst + "x!1"nil nil))
                                nil))
                              nil))
                            nil)
                           ("2" (skosimp)
                            (("2" (inst -3 "c!1")
                              (("2"
                                (split -3)
                                (("1" (propax) nil nil)
                                 ("2" (assertnil nil)
                                 ("3"
                                  (skosimp)
                                  (("3"
                                    (typepred "z!1")
                                    (("3"
                                      (assert)
                                      (("3"
                                        (skosimp)
                                        (("3"
                                          (inst - "x!1")
                                          (("3" (assertnil nil))
                                          nil))
                                        nil))
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                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (hide-all-but 1)
                  (("2" (split)
                    (("1" (expand "nonempty?")
                      (("1" (expand "empty?")
                        (("1" (inst - "abs(f!1(XX))")
                          (("1" (expand "member")
                            (("1" (assert)
                              (("1"
                                (typepred "abs(f!1(XX))")
                                (("1"
                                  (assert)
                                  (("1" (inst + "XX"nil nil))
                                  nil))
                                nil))
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                            nil))
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                        nil))
                      nil)
                     ("2" (typepred "f!1")
                      (("2" (expand "bounded?")
                        (("2" (skosimp)
                          (("2" (expand "above_bounded")
                            (("2" (inst + "c!1")
                              (("2"
                                (expand "upper_bound")
                                (("2"
                                  (skosimp)
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                                    (("2"
                                      (assert)
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                                        (skosimp)
                                        (("2"
                                          (inst - "x!1")
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                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil)
           ("2" (replace 1)
            (("2" (split)
              (("1" (skosimp) (("1" (inst + "x!1"nil nil)) nil)
               ("2" (skosimp*) (("2" (assertnil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((sup_norm const-decl "nnreal" sup_norm nil)
    (nnreal type-eq-decl nil real_types nil)
    (bounded nonempty-type-eq-decl nil sup_norm nil)
    (bounded? const-decl "bool" sup_norm nil)
    (T formal-type-decl nil sup_norm nil)
    (>= const-decl "bool" reals 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)
    (TRUE const-decl "bool" booleans nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (member const-decl "bool" sets nil)
    (empty? const-decl "bool" sets nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (f!1 skolem-const-decl "bounded" sup_norm nil)
    (x!1 skolem-const-decl "T" sup_norm nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (upper_bound const-decl "bool" bound_defs "reals/")
    (pred type-eq-decl nil defined_types nil)
    (least_upper_bound const-decl "bool" bound_defs "reals/")
    (<= const-decl "bool" reals nil) (set type-eq-decl nil sets nil)
    (nonempty? const-decl "bool" sets nil)
    (setof type-eq-decl nil defined_types nil)
    (above_bounded const-decl "bool" bounded_reals "reals/")
    (sup_set type-eq-decl nil bounded_reals "reals/")
    (sup const-decl "{x | least_upper_bound(<=)(x, Su)}" bounded_reals
     "reals/")
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (= const-decl "[T, T -> boolean]" equalities 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)
    (FALSE const-decl "bool" booleans nil)
    (extend const-decl "R" extend nil))
   shostak))
 (sup_norm_convergent_TCC1 0
  (sup_norm_convergent_TCC1-1 nil 3392434594
   ("" (expand "sup_norm_convergent?")
    (("" (inst + "LAMBDA x: 0")
      (("1" (expand "sup_norm_converges_to?")
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                  (("1" (case-replace "EXISTS x: TRUE")
                    (("1"
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              ({c | EXISTS (x_1: T): abs(0) = c}))")
                      (("1"
                        (name-replace "SUP"
                         "sup(extend[real, nnreal, bool, FALSE]
              ({c | EXISTS (x_1: T): abs(0) = c}))")
                        (("1" (expand "extend")
                          (("1" (expand "least_upper_bound")
                            (("1" (flatten)
                              (("1"
                                (expand "upper_bound")
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                                  (inst -2 "0")
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                                      (("3"
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                                            (skosimp)
                                            (("3"
                                              (hide 2 -3)
                                              (("3" (grind) nil nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
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                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (assert)
                      (("2" (replace 1 2) (("2" (assertnil nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (expand "bounded?")
        (("2" (inst + "0") (("2" (grind) nil nil)) nil)) nil))
      nil))
    nil)
   ((bounded? const-decl "bool" sup_norm 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)
    (T formal-type-decl nil sup_norm nil)
    (bounded nonempty-type-eq-decl nil sup_norm nil)
    (sup_norm const-decl "nnreal" sup_norm 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)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (extend const-decl "R" extend nil)
    (FALSE const-decl "bool" booleans nil)
    (nnreal type-eq-decl nil real_types nil)
    (sup const-decl "{x | least_upper_bound(<=)(x, Su)}" bounded_reals
     "reals/")
    (sup_set type-eq-decl nil bounded_reals "reals/")
    (above_bounded const-decl "bool" bounded_reals "reals/")
    (setof type-eq-decl nil defined_types nil)
    (nonempty? const-decl "bool" sets nil)
    (set type-eq-decl nil sets nil) (<= const-decl "bool" reals nil)
    (least_upper_bound const-decl "bool" bound_defs "reals/")
    (pred type-eq-decl nil defined_types nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (int_abs_is_nonneg application-judgement "{j: nonneg_int | j >= i}"
     real_defs nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (real_lt_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)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (upper_bound const-decl "bool" bound_defs "reals/")
    (TRUE const-decl "bool" booleans nil)
    (- const-decl "[T -> real]" real_fun_ops "reals/")
    (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)
    (sup_norm_converges_to? const-decl "bool" sup_norm nil)
    (sup_norm_convergent? const-decl "bool" sup_norm nil))
   nil))
 (sup_norm_convergent_is_pointwise_convergent 0
  (sup_norm_convergent_is_pointwise_convergent-1 nil 3392435448
   ("" (skolem + ("v"))
    (("" (typepred "v")
      (("" (expand "pointwise_convergent?")
        (("" (expand "sup_norm_convergent?")
          (("" (skosimp)
            (("" (inst + "f!1")
              (("" (expand "pointwise_convergence?")
                (("" (skosimp)
                  (("" (expand "sup_norm_converges_to?")
                    (("" (rewrite "metric_convergence_def" *)
                      (("" (expand "metric_converges_to")
                        (("" (skosimp)
                          (("" (inst - "r!1")
                            (("" (skosimp)
                              ((""
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                                ((""
                                  (skosimp)
                                  ((""
                                    (inst - "i!1")
                                    ((""
                                      (assert)
                                      ((""
                                        (expand "ball")
                                        ((""
                                          (expand "sup_norm")
                                          ((""
                                            (case-replace
                                             "EXISTS x: TRUE")
                                            (("1"
                                              (typepred
                                               "sup(extend[real, nnreal, bool, FALSE]
              ({c | EXISTS (x_1: T): abs((v(i!1) - f!1)(x_1)) = c}))")
                                              (("1"
                                                (name-replace
                                                 "SUP"
                                                 "sup(extend[real, nnreal, bool, FALSE]
              ({c | EXISTS (x_1: T): abs((v(i!1) - f!1)(x_1)) = c}))")
                                                (("1"
                                                  (expand
                                                   "least_upper_bound")
                                                  (("1"
                                                    (expand "extend")
                                                    (("1"
                                                      (expand
                                                       "upper_bound")
                                                      (("1"
                                                        (flatten)
                                                        (("1"
                                                          (inst
                                                           -
                                                           "abs(f!1(x!1) - v(i!1)(x!1))")
                                                          (("1"
                                                            (assert)
                                                            nil
                                                            nil)
                                                           ("2"
                                                            (prop)
                                                            (("1"
                                                              (inst
                                                               +
                                                               "x!1")
                                                              (("1"
                                                                (hide-all-but
                                                                 1)
                                                                (("1"
                                                                  (grind)
                                                                  nil
                                                                  nil))
                                                                nil))
                                                              nil)
                                                             ("2"
                                                              (assert)
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("2"
                                              (inst + "x!1")
                                              nil
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((sup_norm_convergent nonempty-type-eq-decl nil sup_norm nil)
    (sup_norm_convergent? const-decl "bool" sup_norm nil)
    (sequence type-eq-decl nil sequences nil)
    (bounded nonempty-type-eq-decl nil sup_norm nil)
    (bounded? const-decl "bool" sup_norm nil)
    (T formal-type-decl nil sup_norm 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)
    (metric_convergence_def formula-decl nil metric_space
     "metric_space/")
    (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)
    (ball_is_metric_open application-judgement
     "metric_open[real, (LAMBDA (x, y: real): abs(x - y))]"
     convergence_aux "metric_space/")
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (member const-decl "bool" sets nil)
    (sup_norm const-decl "nnreal" sup_norm nil)
    (pred type-eq-decl nil defined_types nil)
    (least_upper_bound const-decl "bool" bound_defs "reals/")
    (<= const-decl "bool" reals nil) (set type-eq-decl nil sets nil)
    (nonempty? const-decl "bool" sets nil)
    (setof type-eq-decl nil defined_types nil)
    (above_bounded const-decl "bool" bounded_reals "reals/")
    (sup_set type-eq-decl nil bounded_reals "reals/")
    (sup const-decl "{x | least_upper_bound(<=)(x, Su)}" bounded_reals
     "reals/")
    (nnreal type-eq-decl nil real_types nil)
    (FALSE const-decl "bool" booleans nil)
    (extend const-decl "R" extend nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (- const-decl "[T -> real]" real_fun_ops "reals/")
    (upper_bound const-decl "bool" bound_defs "reals/")
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (f!1 skolem-const-decl "bounded" sup_norm nil)
    (x!1 skolem-const-decl "T" sup_norm nil)
    (v skolem-const-decl "sup_norm_convergent" sup_norm nil)
    (i!1 skolem-const-decl "nat" sup_norm nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (bounded_diff application-judgement "bounded" sup_norm nil)
    (TRUE const-decl "bool" booleans nil)
    (ball const-decl "set[T]" metric_space_def "metric_space/")
    (real_minus_real_is_real application-judgement "real" reals nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (metric_converges_to const-decl "bool" metric_space_def
     "metric_space/")
    (sup_norm_converges_to? const-decl "bool" sup_norm nil)
    (pointwise_convergence? const-decl "bool" pointwise_convergence
     nil)
    (pointwise_convergent? const-decl "bool" pointwise_convergence
     nil))
   nil))
 (sup_norm_converges_to_pointwise_convergence 0
  (sup_norm_converges_to_pointwise_convergence-1 nil 3392527887
   ("" (skosimp)
    (("" (expand "pointwise_convergence?")
      (("" (skosimp)
        (("" (expand "sup_norm_converges_to?")
          (("" (rewrite "metric_convergence_def" *)
            (("" (expand "metric_converges_to")
              (("" (skosimp)
                (("" (inst - "r!1")
                  (("" (skosimp)
                    (("" (inst + "n!1")
                      (("" (skosimp)
                        (("" (inst - "i!1")
                          (("" (assert)
                            (("" (expand "ball")
                              ((""
                                (expand "sup_norm")
                                ((""
                                  (case-replace "EXISTS x: TRUE")
                                  (("1"
                                    (typepred
                                     "sup(extend[real, nnreal, bool, FALSE]
              ({c | EXISTS (x_1: T): abs((u!1(i!1) - f!1)(x_1)) = c}))")
                                    (("1"
                                      (name-replace
                                       "SUP"
                                       "sup(extend[real, nnreal, bool, FALSE]
              ({c | EXISTS (x_1: T): abs((u!1(i!1) - f!1)(x_1)) = c}))")
                                      (("1"
                                        (expand "extend")
                                        (("1"
                                          (expand "least_upper_bound")
                                          (("1"
                                            (flatten)
                                            (("1"
                                              (expand "upper_bound")
                                              (("1"
                                                (inst
                                                 -
                                                 "abs(f!1(x!1) - u!1(i!1)(x!1))")
                                                (("1" (assertnil nil)
                                                 ("2"
                                                  (typepred
                                                   "abs(f!1(x!1) - u!1(i!1)(x!1))")
                                                  (("2"
                                                    (assert)
                                                    (("2"
                                                      (inst + "x!1")
                                                      (("2"
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                                                        (("2"
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                                                          (("2"
                                                            (grind)
                                                            nil
                                                            nil))
                                                          nil))
                                                        nil))
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                                        nil))
                                      nil))
                                    nil)
                                   ("2" (inst + "x!1"nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((pointwise_convergence? const-decl "bool" pointwise_convergence
     nil)
    (sup_norm_converges_to? const-decl "bool" sup_norm nil)
    (metric_converges_to const-decl "bool" metric_space_def
     "metric_space/")
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (ball const-decl "set[T]" metric_space_def "metric_space/")
    (TRUE const-decl "bool" booleans nil)
    (upper_bound const-decl "bool" bound_defs "reals/")
    (minus_real_is_real application-judgement "real" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (i!1 skolem-const-decl "nat" sup_norm nil)
    (u!1 skolem-const-decl "sequence[bounded]" sup_norm nil)
    (x!1 skolem-const-decl "T" sup_norm nil)
    (f!1 skolem-const-decl "bounded" sup_norm nil)
--> --------------------

--> maximum size reached

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

¤ Dauer der Verarbeitung: 0.114 Sekunden  (vorverarbeitet)  ¤





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Die farbliche Syntaxdarstellung ist noch experimentell.


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