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Datei: Abs_Int1_const.thy Sprache: PVS

Original von: PVS^©

(interval_deriv
(deriv_domain_Xt 0
  (deriv_domain_Xt-2 nil 3545779310
   ("" (typepred "X")
    (("" (expand "StrictInterval?")
      (("" (lemma "deriv_domain_closed")
        (("" (inst - "lb(X)" "ub(X)")
          (("" (assert)
            (("" (expand "deriv_domain?")
              (("" (skosimp*)
                (("" (inst - "e!1" "x!1")
                  (("1" (skosimp*)
                    (("1" (inst + "y!1") (("1" (grind) nil nil)) nil))
                    nil)
                   ("2" (assert)
                    (("2" (hide 2)
                      (("2" (typepred "x!1")
                        (("2" (expand "##") (("2" (propax) nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    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_plus_real_is_real application-judgement "real" reals nil)
    (deriv_domain? const-decl "bool" deriv_domain_def "analysis/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (|##| const-decl "bool" interval nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (x!1 skolem-const-decl "Xt" interval_deriv 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)
    (closed_interval type-eq-decl nil intervals_real "reals/")
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (nzreal nonempty-type-eq-decl nil reals nil)
    (/= const-decl "boolean" notequal nil)
    (y!1 skolem-const-decl
     "{u: nzreal | lb(X) <= u + x!1 AND u + x!1 <= ub(X)}"
     interval_deriv nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (deriv_domain_closed formula-decl nil deriv_domain "analysis/")
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (real nonempty-type-from-decl nil reals nil)
    (Interval type-eq-decl nil interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil))
   nil)
  (deriv_domain_Xt-1 nil 3472488588
   ("" (typepred "X")
    (("" (expand "StrictlyProper?")
      (("" (lemma "deriv_domain_closed")
        (("" (inst - "lb(X)" "ub(X)")
          (("" (assert)
            (("" (expand "deriv_domain?")
              (("" (skosimp*)
                (("" (inst - "e!1" "x!1")
                  (("1" (skosimp*)
                    (("1" (inst + "y!1") (("1" (grind) nil nil)) nil))
                    nil)
                   ("2" (assert)
                    (("2" (hide 2)
                      (("2" (typepred "x!1")
                        (("2" (expand "##") (("2" (propax) nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((deriv_domain? const-decl "bool" deriv_domain_def "analysis/")
    (closed_interval type-eq-decl nil intervals_real "reals/")
    (deriv_domain_closed formula-decl nil deriv_domain "analysis/")
    (Interval type-eq-decl nil interval nil))
   nil))
(IMP_derivatives_TCC1 0
  (IMP_derivatives_TCC1-1 nil 3301761309
   ("" (lemma "deriv_domain_Xt") (("" (propax) nil nil)) nil)
   ((deriv_domain_Xt formula-decl nil interval_deriv nil)) shostak))
(IMP_derivatives_TCC2 0
  (IMP_derivatives_TCC2-1 nil 3301761489
   ("" (expand "not_one_element?")
    (("" (skeep)
      (("" (typepred "x")
        (("" (typepred "X")
          (("" (inst 1 "if x=lb(X) then ub(X) else lb(X) endif")
            (("1" (grind) nil nil) ("2" (grind) nil nil)
             ("3" (grind) nil nil))
            nil))
          nil))
        nil))
      nil))
    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 "boolean" notequal nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (x skolem-const-decl "Xt" interval_deriv 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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (not_one_element? const-decl "bool" deriv_domain_def "analysis/"))
   shostak))
(D_TCC1 0
  (D_TCC1-1 nil 3304700431
   ("" (skosimp :preds? t)
    (("" (expand "Diff?") (("" (propax) nil nil)) 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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil))
   shostak))
(Diffn?_TCC1 0
  (Diffn?_TCC1-1 nil 3321368055
   ("" (skosimp*) (("" (assert) nil nil)) nil)
   ((int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   nil))
(Diffn?_TCC2 0
  (Diffn?_TCC2-1 nil 3321368055
   ("" (skosimp*) (("" (assert) nil nil)) nil)
   ((int_minus_int_is_int application-judgement "int" integers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
(Diffn_derivn 0
  (Diffn_derivn-2 nil 3445354344
   ("" (induct "n")
    (("1" (grind) nil nil)
     ("2" (skeep)
      (("2" (skeep)
        (("2" (expand "Diffn?" 1)
          (("2" (expand "derivable_n_times?" 1)
            (("2" (expand "Diff?")
              (("2" (inst -1 "D(f)")
                (("1" (expand "D" -1 2) (("1" (replaces -1) nil nil))
                  nil)
                 ("2" (expand "Diff?") (("2" (assert) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((Diff? const-decl "bool" interval_deriv nil)
    (D const-decl "[Xt -> real]" interval_deriv nil)
    (f skolem-const-decl "[Xt -> real]" interval_deriv nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (derivable_n_times? def-decl "bool" nth_derivatives "analysis/")
    (Diffn? def-decl "bool" interval_deriv nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (StrictInterval type-eq-decl nil interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (|##| const-decl "bool" interval nil)
    (Interval type-eq-decl nil interval nil)
    (pred type-eq-decl nil defined_types 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))
   nil)
  (Diffn_derivn-1 nil 3321368515
   ("" (induct "n")
    (("1" (grind) nil nil)
     ("2" (skeep)
      (("2" (skeep)
        (("2" (expand "Diffn?" 1)
          (("2" (expand "derivable_n_times" 1)
            (("2" (expand "Diff?")
              (("2" (inst -1 "D(f)")
                (("1" (expand "D" -1 2) (("1" (replaces -1) nil nil))
                  nil)
                 ("2" (expand "Diff?") (("2" (assert) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((Interval type-eq-decl nil interval nil)) shostak))
(Dn_TCC1 0
  (Dn_TCC1-1 nil 3321368055 ("" (skosimp*) (("" (assert) nil nil)) nil)
   ((int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   nil))
(Dn_TCC2 0
  (Dn_TCC2-1 nil 3321368055
   ("" (skosimp* :preds? t)
    (("" (expand "Diffn?") (("" (assert) nil nil)) nil)) nil)
   ((real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (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)
    (>= const-decl "bool" 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diffn? def-decl "bool" interval_deriv nil))
   nil))
(Dn_TCC3 0
  (Dn_TCC3-1 nil 3321368055
   ("" (skosimp* :preds? t)
    (("" (expand "Diffn?" -2) (("" (assert) nil nil)) nil)) nil)
   ((real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (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)
    (>= const-decl "bool" 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diffn? def-decl "bool" interval_deriv nil))
   nil))
(Dn_TCC4 0
  (Dn_TCC4-1 nil 3321368055 ("" (skosimp) (("" (assert) nil nil)) nil)
   ((int_minus_int_is_int application-judgement "int" integers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
(Dn_nderiv_TCC1 0
  (Dn_nderiv_TCC1-1 nil 3321368411
   ("" (skosimp* :preds? t)
    (("" (lemma "Diffn_derivn")
      (("" (inst?) (("" (assert) nil nil)) nil)) nil))
    nil)
   ((Diffn_derivn formula-decl nil interval_deriv nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (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)
    (>= const-decl "bool" 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diffn? def-decl "bool" interval_deriv nil))
   nil))
(Dn_nderiv 0
  (Dn_nderiv-1 nil 3321368706
   ("" (induct "n")
    (("1" (grind) nil nil)
     ("2" (skeep)
      (("2" (skeep :preds? t)
        (("2" (expand "Dn" 1)
          (("2" (expand "nderiv" 1)
            (("2" (expand "Diffn?" -1)
              (("2" (flatten)
                (("2" (inst -3 "D(f)")
                  (("2" (expand "D" -3 2) (("2" (propax) nil nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("3" (hide 2)
      (("3" (skeep :preds? t) (("3" (rewrite "Diffn_derivn") nil nil))
        nil))
      nil))
    nil)
   ((Diffn_derivn formula-decl nil interval_deriv nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (D const-decl "[Xt -> real]" interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (nderiv def-decl "[T -> real]" nth_derivatives "analysis/")
    (nderiv_fun type-eq-decl nil nth_derivatives "analysis/")
    (Dn def-decl "[Xt -> real]" interval_deriv nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (pred type-eq-decl nil defined_types 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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diffn? def-decl "bool" interval_deriv nil)
    (derivable_n_times? def-decl "bool" nth_derivatives "analysis/"))
   shostak))
(Diff_id 0
  (Diff_id-1 nil 3304425174
   ("" (expand "Diff?")
    (("" (lemma "derivable_id")
      (("" (expand "I") (("" (propax) nil nil)) nil)) nil))
    nil)
   ((Xt type-eq-decl nil interval_deriv nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (StrictInterval type-eq-decl nil interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (|##| const-decl "bool" interval nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (Interval type-eq-decl nil interval 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)
    (derivable_id judgement-tcc nil derivatives "analysis/")
    (I const-decl "(bijective?[T, T])" identity nil)
    (Diff? const-decl "bool" interval_deriv nil))
   shostak))
(D_id_TCC1 0
  (D_id_TCC1-1 nil 3304424118 ("" (rewrite "Diff_id") nil nil)
   ((Diff_id formula-decl nil interval_deriv nil)) shostak))
(D_id 0
  (D_id-1 nil 3304429116
   ("" (expand "D")
    (("" (lemma "deriv_id_fun")
      (("" (expand "I")
        (("" (expand "const_fun") (("" (propax) nil nil)) nil)) nil))
      nil))
    nil)
   ((Xt type-eq-decl nil interval_deriv nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (StrictInterval type-eq-decl nil interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (|##| const-decl "bool" interval nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (Interval type-eq-decl nil interval 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)
    (deriv_id_fun formula-decl nil derivatives "analysis/")
    (D const-decl "[Xt -> real]" interval_deriv nil))
   shostak))
(Diff_const 0
  (Diff_const-1 nil 3304425582
   ("" (skosimp)
    (("" (expand "Diff?")
      (("" (lemma "derivable_const")
        (("" (inst?)
          (("" (expand "const_fun") (("" (propax) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((Diff? const-decl "bool" interval_deriv nil)
    (const_fun const-decl "[T -> real]" real_fun_ops "reals/")
    (derivable_const judgement-tcc nil derivatives "analysis/")
    (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)
    (Interval type-eq-decl nil interval nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil))
   shostak))
(D_const_TCC1 0
  (D_const_TCC1-1 nil 3304424144
   ("" (skosimp) (("" (rewrite "Diff_const") nil nil)) nil)
   ((Diff_const formula-decl nil interval_deriv 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))
   shostak))
(D_const 0
  (D_const-1 nil 3304430079
   ("" (skosimp)
    (("" (expand "D")
      (("" (lemma "deriv_const_fun")
        (("" (inst -1 "a!1")
          (("" (expand "const_fun") (("" (propax) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((D const-decl "[Xt -> real]" interval_deriv nil)
    (deriv_const_fun formula-decl nil derivatives "analysis/")
    (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)
    (Interval type-eq-decl nil interval nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil))
   shostak))
(Diff_add 0
  (Diff_add-1 nil 3304429143
   ("" (skosimp :preds? t)
    (("" (expand "Diff?")
      (("" (lemma "derivable_sum")
        (("" (inst -1 "f!1" "g!1")
          (("" (expand "+") (("" (propax) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((real_plus_real_is_real application-judgement "real" reals nil)
    (derivable? const-decl "bool" derivatives "analysis/")
    (f!1 skolem-const-decl "(Diff?)" interval_deriv nil)
    (g!1 skolem-const-decl "(Diff?)" interval_deriv nil)
    (deriv_fun type-eq-decl nil derivatives "analysis/")
    (+ const-decl "[T -> real]" real_fun_ops "reals/")
    (derivable_sum judgement-tcc nil derivatives "analysis/")
    (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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil))
   nil))
(D_add_TCC1 0
  (D_add_TCC1-1 nil 3304424494
   ("" (skosimp) (("" (rewrite "Diff_add") nil nil)) nil)
   ((Diff_add formula-decl nil interval_deriv 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)
    (Interval type-eq-decl nil interval nil)
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    (|##| const-decl "bool" interval nil)
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    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil))
   shostak))
(D_add 0
  (D_add-1 nil 3304430121
   ("" (skosimp :preds? t)
    (("" (expand* "Diff?" "D")
      (("" (lemma "deriv_sum_fun")
        (("" (inst -1 "f!1" "g!1")
          (("" (expand "+") (("" (propax) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((D const-decl "[Xt -> real]" interval_deriv nil)
    (derivable? const-decl "bool" derivatives "analysis/")
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    (g!1 skolem-const-decl "(Diff?)" interval_deriv nil)
    (deriv_fun type-eq-decl nil derivatives "analysis/")
    (+ const-decl "[T -> real]" real_fun_ops "reals/")
    (deriv_sum_fun formula-decl nil derivatives "analysis/")
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
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    (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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil))
   shostak))
(Diff_mult 0
  (Diff_mult-1 nil 3304429240
   ("" (skosimp :preds? t)
    (("" (expand "Diff?")
      (("" (lemma "derivable_prod")
        (("" (inst -1 "f!1" "g!1")
          (("" (expand "*") (("" (propax) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((real_times_real_is_real application-judgement "real" reals nil)
    (derivable? const-decl "bool" derivatives "analysis/")
    (f!1 skolem-const-decl "(Diff?)" interval_deriv nil)
    (g!1 skolem-const-decl "(Diff?)" interval_deriv nil)
    (deriv_fun type-eq-decl nil derivatives "analysis/")
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (derivable_prod judgement-tcc nil derivatives "analysis/")
    (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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil))
   shostak))
(D_mult_TCC1 0
  (D_mult_TCC1-1 nil 3304424503
   ("" (skosimp) (("" (rewrite "Diff_mult") nil nil)) nil)
   ((Diff_mult formula-decl nil interval_deriv 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)
    (Interval type-eq-decl nil interval nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (|##| const-decl "bool" interval nil)
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    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
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   shostak))
(D_mult 0
  (D_mult-1 nil 3304430162
   ("" (skosimp :preds? t)
    (("" (expand* "Diff?" "D")
      (("" (lemma "deriv_prod_fun")
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          (("" (expand "*")
            (("" (expand "+") (("" (propax) nil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((D const-decl "[Xt -> real]" interval_deriv nil)
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    (g!1 skolem-const-decl "(Diff?)" interval_deriv nil)
    (deriv_fun type-eq-decl nil derivatives "analysis/")
    (+ const-decl "[T -> real]" real_fun_ops "reals/")
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (deriv_prod_fun formula-decl nil derivatives "analysis/")
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    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
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    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil))
   shostak))
(Diff_pow_TCC1 0
  (Diff_pow_TCC1-1 nil 3305042267 ("" (subtype-tcc) nil nil)
   ((/= const-decl "boolean" notequal nil)) shostak))
(Diff_pow 0
  (Diff_pow-1 nil 3305042471
   ("" (skeep)
    (("" (case "n=0")
      (("1" (replaces)
        (("1" (expand "^")
          (("1" (expand "expt") (("1" (rewrite "Diff_const") nil nil))
            nil))
          nil))
        nil)
       ("2" (expand "Diff?")
        (("2" (lemma "deriv_x_to_n")
          (("2" (inst -1 "n" "1")
            (("1" (beta) (("1" (flatten) (("1" (assert) nil nil)) nil))
              nil)
             ("2" (assert) nil nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((nat nonempty-type-eq-decl nil naturalnumbers nil)
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    (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
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    (= const-decl "[T, T -> boolean]" equalities nil)
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    (Diff_const formula-decl nil interval_deriv nil)
    (expt def-decl "real" exponentiation nil)
    (deriv_x_to_n formula-decl nil derivatives "analysis/")
    (Interval type-eq-decl nil interval nil)
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    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
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    (> const-decl "bool" reals nil)
    (real_gt_is_strict_total_order name-judgement
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    (Diff? const-decl "bool" interval_deriv nil))
   shostak))
(D_pow_TCC1 0
  (D_pow_TCC1-1 nil 3305042277 ("" (subtype-tcc) nil nil)
   ((/= const-decl "boolean" notequal nil)) shostak))
(D_pow_TCC2 0
  (D_pow_TCC2-1 nil 3305042285
   ("" (skosimp) (("" (rewrite "Diff_pow") nil nil)) nil)
   ((Diff_pow formula-decl nil interval_deriv nil)
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    (boolean nonempty-type-decl nil booleans nil)
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    (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)
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    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil))
   shostak))
(D_pow_TCC3 0
  (D_pow_TCC3-1 nil 3305042306 ("" (subtype-tcc) nil nil)
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(D_pow 0
  (D_pow-1 nil 3305042697
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    (("" (expand "D")
      (("" (lemma "deriv_x_to_n")
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          (("" (beta) (("" (flatten) (("" (assert) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((D const-decl "[Xt -> real]" interval_deriv 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)
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    (> const-decl "bool" reals nil)
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    (|##| const-decl "bool" interval nil)
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    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil))
   shostak))
(Diff_scal1 0
  (Diff_scal1-2 nil 3304699767
   ("" (skosimp :preds? t)
    (("" (expand "Diff?")
      (("" (lemma "derivable_scal")
        (("" (inst -1 "a!1" "f!1")
          (("" (expand "*") (("" (propax) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((real_times_real_is_real application-judgement "real" reals nil)
    (derivable? const-decl "bool" derivatives "analysis/")
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    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (derivable_scal judgement-tcc nil derivatives "analysis/")
    (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
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    (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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil))
   nil))
(D_scal1_TCC1 0
  (D_scal1_TCC1-2 nil 3304431213
   ("" (skosimp) (("" (rewrite "Diff_scal1") nil nil)) nil)
   ((Diff_scal1 formula-decl nil interval_deriv nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
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    (real_pred const-decl "[number_field -> boolean]" reals nil)
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    (Interval type-eq-decl nil interval nil)
    (bool nonempty-type-eq-decl nil booleans nil)
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    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil))
   nil))
(D_scal1 0
  (D_scal1-1 nil 3304431129
   ("" (skosimp :preds? t)
    (("" (expand* "Diff?" "D")
      (("" (lemma "deriv_scal_fun")
        (("" (inst -1 "a!1" "f!1")
          (("" (expand "*") (("" (propax) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((D const-decl "[Xt -> real]" interval_deriv nil)
    (derivable? const-decl "bool" derivatives "analysis/")
    (f!1 skolem-const-decl "(Diff?)" interval_deriv nil)
    (deriv_fun type-eq-decl nil derivatives "analysis/")
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (deriv_scal_fun formula-decl nil derivatives "analysis/")
    (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
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    (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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil))
   nil))
(Diff_scal2 0
  (Diff_scal2-1 nil 3304431294
   ("" (skosimp :preds? t)
    (("" (lemma "Diff_scal1")
      (("" (inst -1 "a!1" "f!1") (("" (assert) nil nil)) nil)) nil))
    nil)
   ((Diff_scal1 formula-decl nil interval_deriv nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
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    (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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil))
   shostak))
(D_scal2_TCC1 0
  (D_scal2_TCC1-2 nil 3304431448
   ("" (skosimp) (("" (rewrite "Diff_scal2") nil nil)) nil)
   ((Diff_scal2 formula-decl nil interval_deriv 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)
    (Interval type-eq-decl nil interval nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil))
   nil))
(D_scal2 0
  (D_scal2-1 nil 3304431330
   ("" (skosimp :preds? t)
    (("" (lemma "D_scal1")
      (("" (inst -1 "a!1" "f!1") (("" (assert) nil nil)) nil)) nil))
    nil)
   ((D_scal1 formula-decl nil interval_deriv nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
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    (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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil))
   shostak))
(Diff_neg 0
  (Diff_neg-2 nil 3442593099
   ("" (skosimp :preds? t)
    (("" (expand "Diff?")
      (("" (lemma "derivable_neg")
        (("" (inst -1 "g!1")
          (("" (expand "-") (("" (propax) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((minus_real_is_real application-judgement "real" reals nil)
    (derivable? const-decl "bool" derivatives "analysis/")
    (g!1 skolem-const-decl "(Diff?)" interval_deriv nil)
    (deriv_fun type-eq-decl nil derivatives "analysis/")
    (- const-decl "[T -> real]" real_fun_ops "reals/")
    (derivable_neg judgement-tcc nil derivatives "analysis/")
    (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
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    (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)
    (Interval type-eq-decl nil interval nil)
    (|##| const-decl "bool" interval nil)
    (StrictInterval? const-decl "bool" interval nil)
    (StrictInterval type-eq-decl nil interval nil)
    (X formal-const-decl "StrictInterval" interval_deriv nil)
    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil))
   nil)
  (Diff_neg-1 nil 3304429291
   ("" (skosimp :preds? t)
    (("" (expand "Diff?")
      (("" (lemma "derivable_opp")
        (("" (inst -1 "g!1")
          (("" (expand "-") (("" (propax) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((deriv_fun type-eq-decl nil derivatives "analysis/")
    (Interval type-eq-decl nil interval nil))
   shostak))
(D_neg_TCC1 0
  (D_neg_TCC1-1 nil 3304424526
   ("" (skosimp) (("" (rewrite "Diff_neg") nil nil)) nil)
   ((Diff_neg formula-decl nil interval_deriv 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)
    (Interval type-eq-decl nil interval nil)
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(D_neg 0
  (D_neg-2 nil 3442592991
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      (("" (lemma "deriv_neg_fun")
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      nil))
    nil)
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(Diff_sub 0
  (Diff_sub-1 nil 3304429323
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    (("" (expand "Diff?")
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(D_sub_TCC1 0
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(D_sub 0
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(Diff_sq 0
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(D_sq_TCC1 0
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(D_sq 0
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(Diff_div_TCC1 0
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(Diff_div 0
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(D_div_TCC1 0
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(D_div_TCC2 0
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(D_div 0
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    (* const-decl "[T -> real]" real_fun_ops "reals/")
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    (Xt type-eq-decl nil interval_deriv nil)
    (Diff? const-decl "bool" interval_deriv nil)
    (/= const-decl "boolean" notequal nil))
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(Diff_scald1 0
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    (("" (expand "Diff?")
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           ("2" (assert) nil nil)
           ("3" (hide 2)
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            nil))
          nil))
        nil))
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    (k!1 skolem-const-decl "(LAMBDA (f): FORALL (t: Xt): f(t) /= 0)"
     interval_deriv nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
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    (nzreal nonempty-type-eq-decl nil reals nil)
    (nz_deriv_fun type-eq-decl nil derivatives "analysis/")
    (/ const-decl "[T -> real]" real_fun_ops "reals/")
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(D_scald1_TCC1 0
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(D_scald1 0
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    (real_times_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/")
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (/ const-decl "[T -> real]" real_fun_ops "reals/")
    (/ const-decl "[T -> real]" real_fun_ops "reals/")
    (deriv_scaldiv_fun formula-decl nil derivatives "analysis/")
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--> --------------------

--> maximum size reached

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

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