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Datei: .project Sprache: Lisp

Original von: PVS^©

(sigma_below_sub
(sigma_diff_eq_TCC1 0
  (sigma_diff_eq_TCC1-1 nil 3282393213 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= 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)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
(sigma_diff_eq_TCC2 0
  (sigma_diff_eq_TCC2-1 nil 3282393213 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= 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)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
(sigma_diff_eq_TCC3 0
  (sigma_diff_eq_TCC3-1 nil 3282393213 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= 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)
    (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)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
(sigma_diff_eq_TCC4 0
  (sigma_diff_eq_TCC4-1 nil 3282393213 ("" (assuming-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= 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))
   shostak))
(sigma_diff_eq_TCC5 0
  (sigma_diff_eq_TCC5-1 nil 3282393214 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= 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)
    (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)
    (integer nonempty-type-from-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N1 formal-const-decl "nat" sigma_below_sub nil)
    (< const-decl "bool" reals nil))
   shostak))
(sigma_diff_eq_TCC6 0
  (sigma_diff_eq_TCC6-1 nil 3282393214 ("" (assuming-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= 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)
    (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)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
(sigma_diff_eq_TCC7 0
  (sigma_diff_eq_TCC7-1 nil 3352459362 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= 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))
   nil))
(sigma_diff_eq_TCC8 0
  (sigma_diff_eq_TCC8-1 nil 3352459362 ("" (assuming-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= 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)
    (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)
    (integer nonempty-type-from-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N2 formal-const-decl "nat" sigma_below_sub nil)
    (< const-decl "bool" reals nil))
   nil))
(sigma_diff_eq 0
  (sigma_diff_eq-3 nil 3403453952
   ("" (induct "n")
    (("1" (skosimp*)
      (("1" (expand "sigma")
        (("1" (lift-if)
          (("1" (ground)
            (("1" (inst?)
              (("1" (assert)
                (("1" (expand "sigma") (("1" (propax) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("2" (skosimp*)
      (("2" (expand "sigma" 1)
        (("2" (assert)
          (("2" (inst?)
            (("2" (inst?)
              (("2" (prop)
                (("1" (inst -5 "1+j!1") (("1" (assert) nil nil)) nil)
                 ("2" (assert)
                  (("2" (inst -4 "1+j!1")
                    (("2" (assert)
                      (("2" (assert)
                        (("2" (expand "sigma") (("2" (propax) nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("3" (skosimp*)
                  (("3" (inst?) (("3" (assert) nil nil)) nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("3" (hide 2) (("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil)
     ("4" (hide 2) (("4" (skosimp*) nil nil)) nil)
     ("5" (assert)
      (("5" (hide 2) (("5" (skosimp*) (("5" (assert) nil nil)) nil))
        nil))
      nil)
     ("6" (hide 2) (("6" (skosimp*) (("6" (assert) nil nil)) nil)) nil)
     ("7" (hide 2) (("7" (skosimp*) nil nil)) nil)
     ("8" (assert)
      (("8" (hide 2) (("8" (skosimp*) (("8" (assert) nil nil)) nil))
        nil))
      nil)
     ("9" (hide 2) (("9" (skosimp*) (("9" (assert) nil nil)) nil)) nil)
     ("10" (hide 2) (("10" (skosimp*) (("10" (assert) nil nil)) nil))
      nil))
    nil)
   ((real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields 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_plus_real_is_real application-judgement "real" reals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (sigma def-decl "real" sigma nil)
    (T_high type-eq-decl nil sigma nil)
    (T_low type-eq-decl nil sigma nil)
    (pred type-eq-decl nil defined_types nil)
    (integer nonempty-type-from-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (OR const-decl "[bool, bool -> bool]" booleans 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)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
    (N2 formal-const-decl "nat" sigma_below_sub nil)
    (N1 formal-const-decl "nat" sigma_below_sub nil))
   nil)
  (sigma_diff_eq-2 nil 3282386439
   ("" (induct "n")
    (("1" (skosimp*)
      (("1" (expand "sigma")
        (("1" (lift-if)
          (("1" (ground) (("1" (inst?) (("1" (assert) nil nil)) nil))
            nil))
          nil))
        nil))
      nil)
     ("2" (skosimp*)
      (("2" (expand "sigma" 1)
        (("2" (assert)
          (("2" (inst?)
            (("2" (inst?)
              (("2" (prop)
                (("1" (inst -5 "1+j!1")
                  (("1" (assert)
                    (("1" (lift-if) (("1" (ground) nil nil)) nil))
                    nil))
                  nil)
                 ("2" (assert)
                  (("2" (inst -4 "1+j!1") (("2" (assert) nil nil))
                    nil))
                  nil)
                 ("3" (skosimp*)
                  (("3" (assert)
                    (("3" (inst?) (("3" (assert) nil nil)) nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("3" (hide 2) (("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil)
     ("4" (hide 2) (("4" (skosimp*) nil nil)) nil)
     ("5" (hide 2)
      (("5" (skosimp*)
        (("5" (inst + "0")
          (("1" (assert) nil nil) ("2" (assert) nil nil)) nil))
        nil))
      nil)
     ("6" (hide 2) (("6" (skosimp*) (("6" (assert) nil nil)) nil)) nil)
     ("7" (hide 2) (("7" (skosimp*) nil nil)) nil)
     ("8" (hide 2) (("8" (skosimp*) (("8" (assert) nil nil)) nil)) nil)
     ("9" (hide 2) (("9" (skosimp*) (("9" (assert) nil nil)) nil)) nil)
     ("10" (hide 2) (("10" (skosimp*) (("10" (assert) nil nil)) nil))
      nil))
    nil)
   ((T_low type-eq-decl nil sigma nil)
    (T_high type-eq-decl nil sigma nil)
    (sigma def-decl "real" sigma nil))
   nil)
  (sigma_diff_eq-1 nil 3282385980
   ("" (induct "n")
    (("1" (skosimp*)
      (("1" (expand "sigma")
        (("1" (lift-if) (("1" (ground) nil nil)) nil)) nil))
      nil)
     ("2" (skosimp*)
      (("2" (expand "sigma" 1)
        (("2" (assert)
          (("2" (lift-if)
            (("2" (ground)
              (("1" (inst -6 "n0!1") nil nil)
               ("2" (inst -5 "1+j!1")
                (("2" (assert)
                  (("2" (assert)
                    (("2" (replace -5)
                      (("2" (assert)
                        (("2" (inst?)
                          (("2" (assert) (("2" (postpone) nil nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("3" (hide 2) (("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil)
     ("4" (hide 2) (("4" (skosimp*) (("4" (assert) nil nil)) nil)) nil)
     ("5" (hide 2) (("5" (skosimp*) (("5" (assert) nil nil)) nil)) nil)
     ("6" (hide 2) (("6" (skosimp*) (("6" (assert) nil nil)) nil)) nil)
     ("7" (postpone) nil nil) ("8" (postpone) nil nil))
    nil)
   nil shostak))
(sigma_diff_shift_TCC1 0
  (sigma_diff_shift_TCC1-1 nil 3282393214 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= 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)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
(sigma_diff_shift_TCC2 0
  (sigma_diff_shift_TCC2-1 nil 3282393214 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= 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)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
(sigma_diff_shift_TCC3 0
  (sigma_diff_shift_TCC3-1 nil 3282393215 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= 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)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers 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)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
(sigma_diff_shift_TCC4 0
  (sigma_diff_shift_TCC4-1 nil 3282393215 ("" (assuming-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= 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))
   shostak))
(sigma_diff_shift_TCC5 0
  (sigma_diff_shift_TCC5-1 nil 3282393215 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= 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)
    (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)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (integer nonempty-type-from-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N1 formal-const-decl "nat" sigma_below_sub nil)
    (< const-decl "bool" reals nil))
   shostak))
(sigma_diff_shift_TCC6 0
  (sigma_diff_shift_TCC6-1 nil 3282393216 ("" (assuming-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= 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)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers 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)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
(sigma_diff_shift_TCC7 0
  (sigma_diff_shift_TCC7-1 nil 3352459362
   ("" (skosimp*)
    (("" (inst + "n!1 + m!1")
      (("1" (assert) nil nil) ("2" (assert) nil nil)) nil))
    nil)
   ((real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (N2 formal-const-decl "nat" sigma_below_sub nil)
    (n!1 skolem-const-decl "nat" sigma_below_sub nil)
    (m!1 skolem-const-decl "nat" sigma_below_sub 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)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields 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)
    (below type-eq-decl nil naturalnumbers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   nil))
(sigma_diff_shift_TCC8 0
  (sigma_diff_shift_TCC8-1 nil 3352459362 ("" (assuming-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= 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)
    (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)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (integer nonempty-type-from-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N2 formal-const-decl "nat" sigma_below_sub nil)
    (< const-decl "bool" reals nil))
   nil))
(sigma_diff_shift 0
  (sigma_diff_shift-2 nil 3403453975
   ("" (induct "n")
    (("1" (skosimp*)
      (("1" (expand "sigma")
        (("1" (lift-if)
          (("1" (ground)
            (("1" (inst?)
              (("1" (assert)
                (("1" (expand "sigma") (("1" (propax) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("2" (skosimp*)
      (("2" (expand "sigma" 1)
        (("2" (assert)
          (("2" (inst?)
            (("2" (inst?)
              (("2" (assert)
                (("2" (prop)
                  (("1" (inst -5 "1+j!1") (("1" (assert) nil nil)) nil)
                   ("2" (ground)
                    (("2" (expand "sigma")
                      (("2" (assert)
                        (("2" (inst?) (("2" (assert) nil nil)) nil))
                        nil))
                      nil))
                    nil)
                   ("3" (skosimp*)
                    (("3" (inst?) (("3" (assert) nil nil)) nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("3" (hide 2) (("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil)
     ("4" (hide 2) (("4" (skosimp*) nil nil)) nil)
     ("5" (hide 2) (("5" (skosimp*) (("5" (assert) nil nil)) nil)) nil)
     ("6" (hide 2) (("6" (skosimp*) (("6" (assert) nil nil)) nil)) nil)
     ("7" (hide 2) (("7" (skosimp*) nil nil)) nil)
     ("8" (hide 2) (("8" (skosimp*) (("8" (assert) nil nil)) nil)) nil)
     ("9" (hide 2) (("9" (skosimp*) (("9" (assert) nil nil)) nil)) nil)
     ("10" (hide 2) (("10" (skosimp*) (("10" (assert) nil nil)) nil))
      nil))
    nil)
   ((real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props 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)
    (nat_induction formula-decl nil naturalnumbers nil)
    (sigma def-decl "real" sigma nil)
    (T_high type-eq-decl nil sigma nil)
    (T_low type-eq-decl nil sigma nil)
    (pred type-eq-decl nil defined_types nil)
    (integer nonempty-type-from-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (OR const-decl "[bool, bool -> bool]" booleans 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)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (N2 formal-const-decl "nat" sigma_below_sub nil)
    (N1 formal-const-decl "nat" sigma_below_sub nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil))
   nil)
  (sigma_diff_shift-1 nil 3282392564
   ("" (induct "n")
    (("1" (skosimp*)
      (("1" (expand "sigma")
        (("1" (lift-if)
          (("1" (ground) (("1" (inst?) (("1" (assert) nil nil)) nil))
            nil))
          nil))
        nil))
      nil)
     ("2" (skosimp*)
      (("2" (expand "sigma" 1)
        (("2" (assert)
          (("2" (inst?)
            (("2" (inst?)
              (("2" (assert)
                (("2" (prop)
                  (("1" (inst -5 "1+j!1")
                    (("1" (assert)
                      (("1" (lift-if) (("1" (ground) nil nil)) nil))
                      nil))
                    nil)
                   ("2" (inst -4 "1+j!1") (("2" (assert) nil nil)) nil)
                   ("3" (hide 2)
                    (("3" (skosimp*)
                      (("3" (assert)
                        (("3" (inst?) (("3" (assert) nil nil)) nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("3" (hide 2) (("3" (skosimp*) (("3" (assert) nil nil)) nil)) nil)
     ("4" (hide 2) (("4" (skosimp*) nil nil)) nil)
     ("5" (hide 2) (("5" (skosimp*) (("5" (assert) nil nil)) nil)) nil)
     ("6" (hide 2) (("6" (skosimp*) (("6" (assert) nil nil)) nil)) nil)
     ("7" (hide 2) (("7" (skosimp*) nil nil)) nil)
     ("8" (hide 2) (("8" (skosimp*) (("8" (assert) nil nil)) nil)) nil)
     ("9" (hide 2) (("9" (skosimp*) (("9" (assert) nil nil)) nil)) nil)
     ("10" (hide 2) (("10" (skosimp*) (("10" (assert) nil nil)) nil))
      nil))
    nil)
   ((T_low type-eq-decl nil sigma nil)
    (T_high type-eq-decl nil sigma nil)
    (sigma def-decl "real" sigma nil))
   shostak)))

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