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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: closest_approach_3D.prf   Sprache: Lisp

Original von: PVS©

(poly_system_strategy
 (first_eq_TCC1 0
  (first_eq_TCC1-1 nil 3621331936 ("" (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))
 (first_eq_TCC2 0
  (first_eq_TCC2-1 nil 3621331936 ("" (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)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
 (first_eq_TCC3 0
  (first_eq_TCC3-1 nil 3621331936 ("" (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_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (lt_realorder name-judgement "RealOrder" real_orders "reals/")
    (< const-decl "bool" reals nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (subrange type-eq-decl nil integers nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (> const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil))
   nil))
 (first_eq_TCC4 0
  (first_eq_TCC4-1 nil 3621331936 ("" (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)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (< const-decl "bool" reals nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (subrange type-eq-decl nil integers nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (> const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil))
   nil))
 (first_eq_TCC5 0
  (first_eq_TCC5-1 nil 3621331936 ("" (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_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (< const-decl "bool" reals nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (subrange type-eq-decl nil integers nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (> const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil))
   nil))
 (first_eq_TCC6 0
  (first_eq_TCC6-1 nil 3621331936 ("" (termination-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)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/"))
   nil))
 (first_eq_TCC7 0
  (first_eq_TCC7-1 nil 3621341858 ("" (termination-tcc) nil nilnil
   nil))
 (greatify_poly_TCC1 0
  (greatify_poly_TCC1-1 nil 3622457802 ("" (subtype-tcc) nil nil)
   ((minus_odd_is_odd application-judgement "odd_int" integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/"))
   nil))
 (greatify_rel_TCC1 0
  (greatify_rel_TCC1-1 nil 3621333990 ("" (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)
    (/= const-decl "boolean" notequal nil))
   nil))
 (greatify_def_TCC1 0
  (greatify_def_TCC1-1 nil 3621333990
   ("" (skeep)
    (("" (skeep)
      (("" (expand "greatify_poly_rel")
        (("" (expand "greatify_poly")
          (("" (expand "*")
            (("" (inst - "j")
              (("" (lift-if) (("" (ground) nil nil)) nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((greatify_poly const-decl "[nat -> int]" poly_system_strategy nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (greatify_poly_rel const-decl "[nat -> int]" poly_system_strategy
     nil))
   nil))
 (greatify_def 0
  (greatify_def-1 nil 3621333996
   ("" (skeep)
    (("" (expand "solvable?")
      (("" (expand "solvable_at?")
        (("" (expand "rel5")
          (("" (ground)
            (("1" (skeep)
              (("1" (inst + "x")
                (("1" (skeep)
                  (("1" (inst - "i")
                    (("1" (assert)
                      (("1" (typepred "greatify_rel(RelF6)(i)")
                        (("1" (assert)
                          (("1" (split -)
                            (("1" (flatten)
                              (("1"
                                (expand "greatify_rel" 3 1)
                                (("1"
                                  (assert)
                                  (("1"
                                    (expand "greatify_poly_rel" +)
                                    (("1"
                                      (expand "greatify_poly")
                                      (("1" (propax) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (flatten)
                              (("2"
                                (split -)
                                (("1"
                                  (flatten)
                                  (("1"
                                    (assert)
                                    (("1"
                                      (expand "greatify_rel" 4)
                                      (("1"
                                        (expand "greatify_poly_rel" +)
                                        (("1"
                                          (expand "greatify_poly")
                                          (("1" (propax) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (flatten)
                                  (("2"
                                    (split -)
                                    (("1"
                                      (flatten)
                                      (("1"
                                        (expand "greatify_rel" 5)
                                        (("1"
                                          (assert)
                                          (("1"
                                            (expand
                                             "greatify_poly_rel"
                                             +)
                                            (("1"
                                              (expand "greatify_poly")
                                              (("1"
                                                (rewrite
                                                 "scal_polynomial2")
                                                (("1"
                                                  (assert)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (flatten)
                                      (("2"
                                        (split -)
                                        (("1"
                                          (assert)
                                          (("1"
                                            (flatten)
                                            (("1"
                                              (expand "greatify_rel" 7)
                                              (("1"
                                                (assert)
                                                (("1"
                                                  (expand
                                                   "greatify_poly_rel"
                                                   +)
                                                  (("1"
                                                    (expand
                                                     "greatify_poly")
                                                    (("1"
                                                      (propax)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (flatten)
                                          (("2"
                                            (split -)
                                            (("1"
                                              (flatten)
                                              (("1"
                                                (assert)
                                                (("1"
                                                  (expand
                                                   "greatify_rel"
                                                   7)
                                                  (("1"
                                                    (assert)
                                                    (("1"
                                                      (expand
                                                       "greatify_poly_rel"
                                                       +)
                                                      (("1"
                                                        (expand
                                                         "greatify_poly")
                                                        (("1"
                                                          (propax)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("2"
                                              (flatten)
                                              (("2"
                                                (expand
                                                 "greatify_rel"
                                                 8)
                                                (("2"
                                                  (assert)
                                                  (("2"
                                                    (expand
                                                     "greatify_poly_rel"
                                                     +)
                                                    (("2"
                                                      (expand
                                                       "greatify_poly")
                                                      (("2"
                                                        (rewrite
                                                         "scal_polynomial2")
                                                        (("2"
                                                          (assert)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (skeep)
              (("2" (inst + "x")
                (("2" (skeep)
                  (("2" (inst - "i")
                    (("2" (split 1)
                      (("1" (flatten)
                        (("1" (expand "greatify_rel" -)
                          (("1" (assert)
                            (("1" (expand "greatify_poly_rel")
                              (("1"
                                (expand "greatify_poly")
                                (("1" (propax) nil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil)
                       ("2" (flatten)
                        (("2" (expand "greatify_rel" -)
                          (("2" (assert)
                            (("2" (split +)
                              (("1"
                                (flatten)
                                (("1"
                                  (assert)
                                  (("1"
                                    (expand "greatify_poly_rel")
                                    (("1"
                                      (expand "greatify_poly")
                                      (("1" (propax) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil)
                               ("2"
                                (flatten)
                                (("2"
                                  (split +)
                                  (("1"
                                    (flatten)
                                    (("1"
                                      (assert)
                                      (("1"
                                        (expand "greatify_poly_rel")
                                        (("1"
                                          (expand "greatify_poly")
                                          (("1"
                                            (rewrite
                                             "scal_polynomial2")
                                            (("1" (assertnil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2"
                                    (flatten)
                                    (("2"
                                      (split +)
                                      (("1"
                                        (flatten)
                                        (("1"
                                          (assert)
                                          (("1"
                                            (expand
                                             "greatify_poly_rel")
                                            (("1"
                                              (expand "greatify_poly")
                                              (("1" (propax) nil nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil)
                                       ("2"
                                        (flatten)
                                        (("2"
                                          (assert)
                                          (("2"
                                            (split +)
                                            (("1"
                                              (flatten)
                                              (("1"
                                                (assert)
                                                (("1"
                                                  (expand
                                                   "greatify_poly_rel")
                                                  (("1"
                                                    (expand
                                                     "greatify_poly")
                                                    (("1"
                                                      (propax)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("2"
                                              (flatten)
                                              (("2"
                                                (assert)
                                                (("2"
                                                  (expand
                                                   "greatify_poly_rel")
                                                  (("2"
                                                    (expand
                                                     "greatify_poly")
                                                    (("2"
                                                      (rewrite
                                                       "scal_polynomial2")
                                                      (("2"
                                                        (assert)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((solvable? const-decl "bool" poly_system_strategy nil)
    (rel5 const-decl "bool" poly_system_strategy nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (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)
    (lt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_times_real_is_real application-judgement "real" reals nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (scal_polynomial2 formula-decl nil polynomials "reals/")
    (sequence type-eq-decl nil sequences nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (greatify_poly const-decl "[nat -> int]" poly_system_strategy nil)
    (greatify_poly_rel const-decl "[nat -> int]" poly_system_strategy
     nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (subrange type-eq-decl nil integers nil)
    (/= const-decl "boolean" notequal nil)
    (greatify_rel const-decl
     "{pz: subrange(0, 5) | pz /= 2 AND pz /= 5}" poly_system_strategy
     nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (solvable_at? const-decl "bool" poly_system_strategy nil))
   shostak))
 (compute_solvable_single_TCC1 0
  (compute_solvable_single_TCC1-1 nil 3621353314
   ("" (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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (subrange type-eq-decl nil integers nil)
    (/= const-decl "boolean" notequal nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/"))
   nil))
 (compute_solvable_single_TCC2 0
  (compute_solvable_single_TCC2-1 nil 3621353314
   ("" (subtype-tcc) nil nil)
   ((/= const-decl "boolean" notequal nil)
    (array2list const-decl
                "{l: listn(n) | FORALL (i: below(n)): a(i) = nth(l, i)}"
                array2list "structures/")
    (base_list const-decl "listn[below(n)](digits)" base_repr "reals/")
    (sturm_tarski_faster const-decl "{r: real |
         r = NSol_all(k, a, m, p, n, RelF6) AND
          rational_pred(r) AND integer_pred(r)}" system_solvers nil)
    (odd? const-decl "bool" integers nil)
    (poly_deriv const-decl "real" polynomials "reals/")
    (int_plus_int_is_int application-judgement "int" integers nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (even_times_int_is_even application-judgement "even_int" integers
     nil))
   nil))
 (compute_solvable_single_TCC3 0
  (compute_solvable_single_TCC3-1 nil 3621353314
   ("" (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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (subrange type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (rel5 const-decl "bool" poly_system_strategy nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/")
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (/= const-decl "boolean" notequal nil)
    (array2list const-decl
                "{l: listn(n) | FORALL (i: below(n)): a(i) = nth(l, i)}"
                array2list "structures/")
    (base_list const-decl "listn[below(n)](digits)" base_repr "reals/")
    (sturm_tarski_faster const-decl "{r: real |
         r = NSol_all(k, a, m, p, n, RelF6) AND
          rational_pred(r) AND integer_pred(r)}" system_solvers nil)
    (odd? const-decl "bool" integers nil)
    (poly_deriv const-decl "real" polynomials "reals/")
    (even_times_int_is_even application-judgement "even_int" integers
     nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil))
   nil))
 (compute_solvable_single_TCC4 0
  (compute_solvable_single_TCC4-1 nil 3621354679
   ("" (skosimp*)
    (("" (lift-if)
      (("" (split -)
        (("1" (flatten)
          (("1" (replaces -2) (("1" (assertnil nil)) nil)) nil)
         ("2" (flatten)
          (("2" (replaces -1)
            (("2" (expand "*") (("2" (propax) nil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((minus_odd_is_odd application-judgement "odd_int" integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/"))
   nil))
 (compute_solvable_single_TCC5 0
  (compute_solvable_single_TCC5-1 nil 3621354679
   ("" (skosimp*)
    (("" (lift-if)
      (("" (split -)
        (("1" (flatten)
          (("1" (replaces -2) (("1" (assertnil nil)) nil)) nil)
         ("2" (flatten)
          (("2" (replaces -1)
            (("2" (expand "*") (("2" (assertnil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((minus_odd_is_odd application-judgement "odd_int" integers nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/"))
   nil))
 (compute_solvable_single_def 0
  (compute_solvable_single_def-1 nil 3621354856
   ("" (skeep)
    (("" (skeep)
      (("" (expand "compute_solvable_single")
        (("" (lift-if)
          (("" (split +)
            (("1" (flatten)
              (("1" (replace -1)
                (("1" (assert) (("1" (grind) nil nil)) nil)) nil))
              nil)
             ("2" (flatten)
              (("2" (assert)
                (("2" (split +)
                  (("1" (flatten)
                    (("1" (assert)
                      (("1" (replace -1)
                        (("1" (name "x1" "-a(0)/a(1)-1")
                          (("1" (name "x2" "-a(0)/a(1)+1")
                            (("1"
                              (case "(polynomial(a,1)(x1)>0 AND polynomial(a,1)(x2)<0) OR (polynomial(a,1)(x1)<0 AND polynomial(a,1)(x2)>0)")
                              (("1"
                                (inst-cp + "x1")
                                (("1"
                                  (inst-cp + "x2")
                                  (("1"
                                    (inst + "-a(0)/a(1)")
                                    (("1" (grind) nil nil))
                                    nil))
                                  nil))
                                nil)
                               ("2"
                                (hide 2)
                                (("2"
                                  (flatten)
                                  (("2" (grind) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (flatten)
                    (("2" (assert)
                      (("2" (split +)
                        (("1" (flatten)
                          (("1" (lemma "system_roots_enum")
                            (("1"
                              (inst - "0" "LAMBDA (k): d"
                               "LAMBDa (k): a")
                              (("1"
                                (assert)
                                (("1"
                                  (skeep -)
                                  (("1"
                                    (case "K = 0")
                                    (("1"
                                      (inst + "0")
                                      (("1"
                                        (inst -4 "0" "0")
                                        (("1"
                                          (assert)
                                          (("1"
                                            (replace -5 +)
                                            (("1"
                                              (expand "rel5")
                                              (("1"
                                                (assert)
                                                (("1"
                                                  (skosimp*)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (inst + "enum(K-1)+2")
                                      (("1"
                                        (replace -4 +)
                                        (("1"
                                          (expand "rel5")
                                          (("1"
                                            (inst -3 "2+enum(K-1)" "0")
                                            (("1"
                                              (assert)
                                              (("1"
                                                (skosimp*)
                                                (("1"
                                                  (inst - "i!1" "K-1")
                                                  (("1"
                                                    (ground)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("2" (assertnil nil))
                                            nil))
                                          nil))
                                        nil)
                                       ("2" (assertnil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (flatten)
                          (("2"
                            (case "NOT ((sturm_tarski_faster(1,
                                                                                           a,
                                                                                           d,
                                                                                           LAMBDA (k): LAMBDA (j): 1,
                                                                                           LAMBDA (k): 0,
                                                                                           LAMBDA (j): 1)
                                                             /= 0) IFF (EXISTS (x:real): polynomial(a,d)(x)=0))")
                            (("1" (hide 3)
                              (("1"
                                (typepred
                                 "sturm_tarski_faster(1,
                                       a,
                                       d,
                                       LAMBDA (k): LAMBDA (j): 1,
                                       LAMBDA (k): 0,
                                       LAMBDA (j): 1)")
                                (("1"
                                  (replaces -1)
                                  (("1"
                                    (hide -)
                                    (("1"
                                      (expand "NSol_all")
                                      (("1"
                                        (lemma "empty_card[real]")
                                        (("1"
                                          (inst?)
                                          (("1"
                                            (assert)
                                            (("1"
                                              (expand "empty?")
                                              (("1"
                                                (expand "member")
                                                (("1"
                                                  (ground)
                                                  (("1"
                                                    (skosimp*)
                                                    (("1"
                                                      (inst - "x!1")
                                                      (("1"
                                                        (expand
                                                         "Sol_all"
                                                         +)
                                                        (("1"
                                                          (assert)
                                                          (("1"
                                                            (hide -)
                                                            (("1"
                                                              (grind)
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil)
                                                   ("2"
                                                    (skosimp*)
                                                    (("2"
                                                      (inst + "x!1")
                                                      (("2"
                                                        (expand
                                                         "Sol_all"
                                                         -)
                                                        (("2"
                                                          (flatten)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (replace -1)
                              (("2"
                                (case "i = 0")
                                (("1"
                                  (replaces -1)
                                  (("1"
                                    (expand "rel5")
                                    (("1" (propax) nil nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (assert)
                                  (("2"
                                    (label "izero" 1)
                                    (("2"
                                      (hide "izero")
                                      (("2"
                                        (split +)
                                        (("1"
                                          (flatten)
                                          (("1"
                                            (assert)
                                            (("1"
                                              (hide -2)
                                              (("1"
                                                (skosimp*)
                                                (("1"
                                                  (inst + "x!1")
                                                  (("1"
                                                    (expand "rel5")
                                                    (("1"
                                                      (ground)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (flatten +)
                                          (("2"
                                            (split 2)
                                            (("1"
                                              (flatten)
                                              (("1"
                                                (case
                                                 "NOT (i = 0 OR i = 1 OR i=2 OR i=3 OR i=4 OR i=5)")
                                                (("1"
                                                  (flatten)
                                                  (("1"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (assert)
                                                  (("2"
                                                    (split -)
                                                    (("1"
                                                      (replace -1)
                                                      (("1"
                                                        (expand "rel5")
                                                        (("1"
                                                          (assert)
                                                          (("1"
                                                            (replace
                                                             -1)
                                                            (("1"
                                                              (case
                                                               "NOT greatify_rel(LAMBDA (j): 1) = (LAMBDA (j): 1)")
                                                              (("1"
                                                                (hide-all-but
                                                                 1)
                                                                (("1"
                                                                  (decompose-equality
                                                                   1)
                                                                  (("1"
                                                                    (expand
                                                                     "greatify_rel")
                                                                    (("1"
                                                                      (propax)
                                                                      nil
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (replaces
                                                                 -1)
                                                                (("2"
                                                                  (assert)
                                                                  (("2"
                                                                    (split
                                                                     1)
                                                                    (("1"
                                                                      (flatten)
                                                                      (("1"
                                                                        (lemma
                                                                         "strict_poly_system_solvable")
                                                                        (("1"
                                                                          (inst
                                                                           -
                                                                           "0"
                                                                           "LAMBDA (ii:nat): d"
                                                                           "LAMBDA (ii:nat): a")
                                                                          (("1"
                                                                            (assert)
                                                                            (("1"
                                                                              (flatten
                                                                               -1)
                                                                              (("1"
                                                                                (hide
                                                                                 -2)
                                                                                (("1"
                                                                                  (split
                                                                                   -1)
                                                                                  (("1"
                                                                                    (inst
                                                                                     -
                                                                                     "0")
                                                                                    (("1"
                                                                                      (assert)
                                                                                      nil
                                                                                      nil))
                                                                                    nil)
                                                                                   ("2"
                                                                                    (inst
                                                                                     -1
                                                                                     "0")
                                                                                    (("2"
                                                                                      (assert)
                                                                                      nil
                                                                                      nil))
                                                                                    nil)
                                                                                   ("3"
                                                                                    (hide
                                                                                     3)
                                                                                    (("3"
                                                                                      (skosimp*)
                                                                                      (("3"
                                                                                        (expand
                                                                                         "sigma")
                                                                                        (("3"
                                                                                          (expand
                                                                                           "sigma")
                                                                                          (("3"
                                                                                            (assert)
                                                                                            (("3"
                                                                                              (typepred
                                                                                               "sturm_tarski_faster(1,
                                                                                                         poly_deriv(a),
                                                                                                         d - 1,
                                                                                                         LAMBDA (j): a,
                                                                                                         LAMBDA (j): d,
                                                                                                         LAMBDA (j): 1)")
                                                                                              (("3"
                                                                                                (hide
                                                                                                 (-2
                                                                                                  -3))
                                                                                                (("3"
                                                                                                  (replaces
                                                                                                   -1)
                                                                                                  (("3"
                                                                                                    (assert)
                                                                                                    (("3"
                                                                                                      (expand
                                                                                                       "NSol_all"
                                                                                                       -)
                                                                                                      (("3"
                                                                                                        (lemma
                                                                                                         "empty_card[real]")
                                                                                                        (("3"
                                                                                                          (inst?)
                                                                                                          (("3"
                                                                                                            (assert)
                                                                                                            (("3"
                                                                                                              (expand
                                                                                                               "empty?")
                                                                                                              (("3"
                                                                                                                (inst
                                                                                                                 -
                                                                                                                 "x!1")
                                                                                                                (("3"
                                                                                                                  (expand
                                                                                                                   "member")
                                                                                                                  (("3"
                                                                                                                    (expand
                                                                                                                     "Sol_all"
                                                                                                                     +)
                                                                                                                    (("3"
                                                                                                                      (assert)
                                                                                                                      (("3"
                                                                                                                        (split)
                                                                                                                        (("1"
                                                                                                                          (replace
                                                                                                                           -2
                                                                                                                           1
                                                                                                                           :dir
                                                                                                                           rl)
                                                                                                                          (("1"
                                                                                                                            (rewrite
                                                                                                                             "poly_eq_le_degree")
                                                                                                                            (("1"
                                                                                                                              (hide
                                                                                                                               2)
                                                                                                                              (("1"
                                                                                                                                (skosimp*)
                                                                                                                                (("1"
                                                                                                                                  (expand
                                                                                                                                   "poly_deriv"
                                                                                                                                   +)
                                                                                                                                  (("1"
--> --------------------

--> maximum size reached

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

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