Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/PVS/trig_fnd/   (Beweissystem der NASA Version 6.0.9©)  Datei vom 28.9.2014 mit Größe 1 kB image not shown  

Quelle  tarski_query_matrix.prf   Sprache: Lisp

 
(tarski_query_matrix
 (TQ_vect3k_TCC1 0
  (TQ_vect3k_TCC1-1 nil 3620050327
   ("" (skeep)
    (("" (skosimp*)
      (("" (replaces -1)
        (("" (assert)
          (("" (lemma "base_n_lt_n")
            (("" (lemma "columns_form_matrix")
              (("" (inst?)
                (("" (assert)
                  (("" (lemma "base_n_lt_n")
                    (("" (inst?) (("" (assertnil nil)) nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (posint_exp application-judgement "posint" exponentiation nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (columns_form_matrix formula-decl nil matrices "matrices/")
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (> const-decl "bool" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props 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)
    (base_n_lt_n formula-decl nil base_repr "reals/"))
   nil))
 (TQ_vect3k_TCC2 0
  (TQ_vect3k_TCC2-1 nil 3621088362
   ("" (skeep)
    (("" (skeep)
      (("" (rewrite "rows_form_matrix")
        (("" (lemma "columns_form_matrix")
          (("" (inst?) (("" (assertnil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((columns_form_matrix formula-decl nil matrices "matrices/")
    (form_matrix_square application-judgement "FullMatrix" matrices
     "matrices/")
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (^ const-decl "real" exponentiation nil)
    (/= const-decl "boolean" notequal nil)
    (OR const-decl "[bool, bool -> bool]" booleans 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)
    (rows_form_matrix formula-decl nil matrices "matrices/")
    (posint_exp application-judgement "posint" exponentiation nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil))
   nil))
 (TQ_vect6k_TCC1 0
  (TQ_vect6k_TCC1-1 nil 3620494852
   ("" (skeep)
    (("" (skeep)
      (("" (skeep)
        (("" (case "x1<=k")
          (("1" (inst + "x1")
            (("1" (replace -2 +)
              (("1" (assert) (("1" (assertnil nil)) nil)) nil))
            nil)
           ("2" (assert)
            (("2" (case "GPFun(i1,j1)(x1)=0")
              (("1" (assertnil nil)
               ("2" (replaces -1)
                (("2" (assert)
                  (("2" (assert)
                    (("2" (lemma "base_n_0")
                      (("2" (inst?)
                        (("2" (assert)
                          (("2" (lemma "both_sides_expt_gt1_le_aux")
                            (("2" (inst - "6" "k" "x1-1")
                              (("2"
                                (expand "^")
                                (("2" (assertnil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    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 "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)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posint_exp application-judgement "posint" exponentiation nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (x1 skolem-const-decl "nat" tarski_query_matrix nil)
    (k skolem-const-decl "nat" tarski_query_matrix nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (base_n_0 formula-decl nil base_repr "reals/")
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (posnat_expt application-judgement "posnat" exponentiation nil)
    (^ const-decl "real" exponentiation nil)
    (both_sides_expt_gt1_le_aux formula-decl nil exponentiation nil)
    (> const-decl "bool" reals nil))
   nil))
 (TQ_vect6k_TCC2 0
  (TQ_vect6k_TCC2-1 nil 3620494852
   ("" (skeep)
    (("" (skeep)
      (("" (rewrite "rows_form_matrix")
        (("" (assert)
          (("" (lemma "columns_form_matrix")
            (("" (inst?) (("" (assertnil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((form_matrix_square application-judgement "FullMatrix" matrices
     "matrices/")
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (columns_form_matrix formula-decl nil matrices "matrices/")
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (^ const-decl "real" exponentiation nil)
    (/= const-decl "boolean" notequal nil)
    (OR const-decl "[bool, bool -> bool]" booleans 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)
    (rows_form_matrix formula-decl nil matrices "matrices/")
    (posint_exp application-judgement "posint" exponentiation nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil))
   nil))
 (NSol_vect3k_TCC1 0
  (NSol_vect3k_TCC1-1 nil 3620051889
   ("" (skosimp*)
    (("" (lemma "base_n_lt_n")
      (("" (inst?) (("" (assertnil nil)) nil)) nil))
    nil)
   ((base_n_lt_n formula-decl nil base_repr "reals/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (posint_exp application-judgement "posint" exponentiation 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)
    (> 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)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
 (NSol_vect3k_TCC2 0
  (NSol_vect3k_TCC2-1 nil 3621088362
   ("" (skeep)
    (("" (rewrite "rows_form_matrix")
      (("" (lemma "columns_form_matrix")
        (("" (inst?) (("" (assertnil nil)) nil)) nil))
      nil))
    nil)
   ((nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (posint_exp application-judgement "posint" exponentiation nil)
    (rows_form_matrix formula-decl nil matrices "matrices/")
    (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)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (^ const-decl "real" exponentiation nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (naturalnumber type-eq-decl nil naturalnumbers nil)
    (form_matrix_square application-judgement "FullMatrix" matrices
     "matrices/")
    (columns_form_matrix formula-decl nil matrices "matrices/"))
   nil))
 (NSol_vect6k_TCC1 0
  (NSol_vect6k_TCC1-1 nil 3620139071
   ("" (skosimp*)
    (("" (lemma "base_n_lt_n")
      (("" (inst?) (("" (assertnil nil)) nil)) nil))
    nil)
   ((base_n_lt_n formula-decl nil base_repr "reals/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (posint_exp application-judgement "posint" exponentiation 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)
    (> 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)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
 (NSol_vect6k_TCC2 0
  (NSol_vect6k_TCC2-1 nil 3621088362
   ("" (skeep)
    (("" (rewrite "rows_form_matrix")
      (("" (assert)
        (("" (lemma "columns_form_matrix")
          (("" (inst?) (("" (assertnil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (posint_exp application-judgement "posint" exponentiation nil)
    (rows_form_matrix formula-decl nil matrices "matrices/")
    (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)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (^ const-decl "real" exponentiation nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (naturalnumber type-eq-decl nil naturalnumbers nil)
    (columns_form_matrix formula-decl nil matrices "matrices/")
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (form_matrix_square application-judgement "FullMatrix" matrices
     "matrices/"))
   nil))
 (A66_inv_TCC1 0
  (A66_inv_TCC1-1 nil 3620408236 ("" (grind) nil nil)
   ((listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/")
    (every adt-def-decl "boolean" list_adt nil))
   nil))
 (A66_inv_TCC2 0
  (A66_inv_TCC2-1 nil 3620408236 ("" (grind) nil nil)
   ((minus_odd_is_odd application-judgement "odd_int" integers nil)
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/")
    (every adt-def-decl "boolean" list_adt nil))
   nil))
 (A66_inv_TCC3 0
  (A66_inv_TCC3-1 nil 3620408236 ("" (eval-formula) nil nil)
   ((TRUE const-decl "bool" booleans nil)
    (id const-decl "(bijective?[T, T])" identity nil)
    (bijective? const-decl "bool" functions nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   nil))
 (A66_TCC1 0
  (A66_TCC1-1 nil 3621152270
   ("" (skeep) (("" (eval-formula) nil nil)) nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (bijective? const-decl "bool" functions nil)
    (id const-decl "(bijective?[T, T])" identity nil)
    (TRUE const-decl "bool" booleans nil))
   nil))
 (A66_TCC2 0
  (A66_TCC2-1 nil 3621152270 ("" (grind) nil nil)
   ((minus_odd_is_odd application-judgement "odd_int" integers nil)
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/")
    (every adt-def-decl "boolean" list_adt nil))
   nil))
 (A66_TCC3 0
  (A66_TCC3-1 nil 3621152270 ("" (grind) nil nil)
   ((posrat_div_posrat_is_posrat application-judgement "posrat"
     rationals nil)
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/")
    (nzrat_div_nzrat_is_nzrat application-judgement "nzrat" rationals
     nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (every adt-def-decl "boolean" list_adt nil))
   nil))
 (A66_TCC4 0
  (A66_TCC4-1 nil 3621152270 ("" (eval-formula) nil nil)
   ((TRUE const-decl "bool" booleans nil)
    (id const-decl "(bijective?[T, T])" identity nil)
    (bijective? const-decl "bool" functions nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   nil))
 (multi_sturm_tarski_6by6 0
  (multi_sturm_tarski_6by6-1 nil 3620495242
   ("" (skeep)
    (("" (case "2<3^(1+k) AND 3^(1+k)<6^(1+k)")
      (("1" (label "2lem" -1)
        (("1" (hide "2lem")
          (("1" (rewrite "full_matrix_eq" +)
            (("1" (invoke (case "NOT %1") (! 2 1))
              (("1" (hide 3)
                (("1" (rewrite "rows_mult")
                  (("1" (assert)
                    (("1" (lemma "tensor_power_rows_alt")
                      (("1" (inst?)
                        (("1" (replaces -1 :dir rl)
                          (("1" (assertnil nil)) nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("2" (replace -1)
                (("2" (invoke (case "NOT %1") (! 2 1))
                  (("1" (hide (-1 3))
                    (("1" (rewrite "columns_mult")
                      (("1" (assertnil nil)
                       ("2" (lemma "tensor_power_rows_alt")
                        (("2" (inst?)
                          (("2" (expand "rows" -1 2)
                            (("2" (expand "length" -1)
                              (("2" (assertnil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (replace -1)
                    (("2" (skeep)
                      (("2" (typepred "j")
                        (("2" (typepred "i")
                          (("2" (case "NOT i < 6^(k+1)")
                            (("1" (assertnil nil)
                             ("2" (case "NOT j = 0")
                              (("1" (assertnil nil)
                               ("2"
                                (replace -1)
                                (("2"
                                  (assert)
                                  (("2"
                                    (rewrite "entry_mult")
                                    (("2"
                                      (assert)
                                      (("2"
                                        (lemma "tensor_power_rows_alt")
                                        (("2"
                                          (inst?)
                                          (("2"
                                            (assert)
                                            (("2"
                                              (lemma "dot_eq_sigma")
                                              (("2"
                                                (expand "*" + 1)
                                                (("2"
                                                  (rewrite -1 +)
                                                  (("2"
                                                    (expand
                                                     "TQ_vect6k"
                                                     +)
                                                    (("2"
                                                      (rewrite
                                                       "entry_form_matrix")
                                                      (("1"
                                                        (case
                                                         "EXISTS (p: upto(k)): base_n(6, i)(p) > 2")
                                                        (("1"
                                                          (replace -1)
                                                          (("1"
                                                            (rewrite
                                                             "length_row"
                                                             +)
                                                            (("1"
                                                              (rewrite
                                                               "length_col"
                                                               +)
                                                              (("1"
                                                                (assert)
                                                                (("1"
                                                                  (lemma
                                                                   "tensor_power_columns_alt")
                                                                  (("1"
                                                                    (inst?)
                                                                    (("1"
                                                                      (assert)
                                                                      (("1"
                                                                        (replace
                                                                         -1
                                                                         :dir
                                                                         rl)
                                                                        (("1"
                                                                          (expand
                                                                           "min"
                                                                           +)
                                                                          (("1"
                                                                            (case
                                                                             "NOT columns(A66_inv) = 6")
                                                                            (("1"
                                                                              (assert)
                                                                              nil
                                                                              nil)
                                                                             ("2"
                                                                              (replace
                                                                               -1)
                                                                              (("2"
                                                                                (assert)
                                                                                (("2"
                                                                                  (lemma
                                                                                   "mult_tarski_query_simple_6_above_2")
                                                                                  (("2"
                                                                                    (inst
                                                                                     -
                                                                                     "GF"
                                                                                     "KF"
                                                                                     "base_n(6,i)"
                                                                                     "a"
                                                                                     "k"
                                                                                     "n")
                                                                                    (("1"
                                                                                      (assert)
                                                                                      (("1"
                                                                                        (replace
                                                                                         -4)
                                                                                        (("1"
                                                                                          (replace
                                                                                           -13)
                                                                                          (("1"
                                                                                            (invoke
                                                                                             (case
                                                                                              "%1 = %2")
                                                                                             (!
                                                                                              -1
                                                                                              1)
                                                                                             (!
                                                                                              2
                                                                                              2))
                                                                                            (("1"
                                                                                              (assert)
                                                                                              nil
                                                                                              nil)
                                                                                             ("2"
                                                                                              (hide
                                                                                               (-1
                                                                                                3))
                                                                                              (("2"
                                                                                                (rewrite
                                                                                                 "sigma_eq")
                                                                                                (("1"
                                                                                                  (hide
                                                                                                   2)
                                                                                                  (("1"
                                                                                                    (skosimp*)
                                                                                                    (("1"
                                                                                                      (case
                                                                                                       "FORALL (a1,a2,b1,b2:real): a1=b1 AND a2=b2 IMPLIES a1*a2 = b1*b2")
                                                                                                      (("1"
                                                                                                        (rewrite
                                                                                                         -1
                                                                                                         1)
                                                                                                        (("1"
                                                                                                          (hide
                                                                                                           2)
                                                                                                          (("1"
                                                                                                            (rewrite
                                                                                                             "access_row")
                                                                                                            (("1"
                                                                                                              (lemma
                                                                                                               "tensor_entry")
                                                                                                              (("1"
                                                                                                                (inst?)
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  (("1"
                                                                                                                    (replaces
                                                                                                                     -1)
                                                                                                                    (("1"
                                                                                                                      (expand
                                                                                                                       "sign_coeff6_zero")
                                                                                                                      (("1"
                                                                                                                        (rewrite
                                                                                                                         "product_eq")
                                                                                                                        (("1"
                                                                                                                          (hide
                                                                                                                           2)
                                                                                                                          (("1"
                                                                                                                            (skosimp*)
                                                                                                                            (("1"
                                                                                                                              (case
                                                                                                                               "NOT rows(A66_inv)=6")
                                                                                                                              (("1"
                                                                                                                                (assert)
                                                                                                                                nil
                                                                                                                                nil)
                                                                                                                               ("2"
                                                                                                                                (replace
                                                                                                                                 -1)
                                                                                                                                (("2"
                                                                                                                                  (assert)
                                                                                                                                  (("2"
                                                                                                                                    (replace
                                                                                                                                     -3)
                                                                                                                                    (("2"
                                                                                                                                      (expand
                                                                                                                                       "entry_pick"
                                                                                                                                       +)
                                                                                                                                      (("2"
                                                                                                                                        (case
                                                                                                                                         "NOT FORALL (ii1,jj2:upto(5)): IF ii1 = 0
                                          THEN (IF jj2 >= 3 THEN 0 ELSE 1 ENDIF)
                                        ELSIF ii1 = 1
                                          THEN (IF jj2 = 1 THEN 1
                                                ELSIF jj2 = 2 THEN -1
                                                ELSE 0
                                                ENDIF)
                                        ELSIF ii1 = 2
                                          THEN (IF 1 <= jj2 AND jj2 <= 2
                                                  THEN 1
                                                ELSE 0
                                                ENDIF)
                                        ELSIF ii1 = 3
                                          THEN (IF 1 <= jj2 AND jj2 <= 2
                                                  THEN -1
                                                ELSIF jj2 = 3 THEN 1
                                                ELSE 0
                                                ENDIF)
                                        ELSIF ii1 = 4
                                          THEN (IF jj2 <= 1 THEN -1
                                                ELSIF jj2 = 4 THEN 1
                                                ELSE 0
                                                ENDIF)
                                        ELSIF ii1 = 5
                                          THEN (IF jj2 = 0 OR jj2 = 2 THEN -1
                                                ELSIF jj2 = 5 THEN 1
                                                ELSE 0
                                                ENDIF)
                                        ELSE 0
                                        ENDIF
                                         = entry(A66_inv)(ii1, jj2)")
                                                                                                                                        (("1"
                                                                                                                                          (hide-all-but
                                                                                                                                           1)
                                                                                                                                          (("1"
                                                                                                                                            (eval-formula)
                                                                                                                                            nil
                                                                                                                                            nil))
                                                                                                                                          nil)
                                                                                                                                         ("2"
                                                                                                                                          (expand
                                                                                                                                           "sign_coeff6_zero_entry"
                                                                                                                                           +)
                                                                                                                                          (("2"
                                                                                                                                            (inst
                                                                                                                                             -
                                                                                                                                             "base_n(6,i)(n!2)"
                                                                                                                                             "base_n(6,n!1)(n!2)")
                                                                                                                                            (("1"
                                                                                                                                              (assert)
                                                                                                                                              (("1"
                                                                                                                                                (hide-all-but
                                                                                                                                                 1)
                                                                                                                                                (("1"
                                                                                                                                                  (lemma
                                                                                                                                                   "base_n_lt_n")
                                                                                                                                                  (("1"
                                                                                                                                                    (inst?)
                                                                                                                                                    (("1"
                                                                                                                                                      (assert)
                                                                                                                                                      nil
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil)
                                                                                                                                             ("2"
                                                                                                                                              (hide-all-but
                                                                                                                                               1)
                                                                                                                                              (("2"
                                                                                                                                                (lemma
                                                                                                                                                 "base_n_lt_n")
                                                                                                                                                (("2"
                                                                                                                                                  (inst?)
                                                                                                                                                  (("2"
                                                                                                                                                    (assert)
                                                                                                                                                    nil
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil)
                                                                                                                         ("2"
                                                                                                                          (hide
                                                                                                                           2)
                                                                                                                          (("2"
                                                                                                                            (hide-all-but
                                                                                                                             1)
                                                                                                                            (("2"
                                                                                                                              (lemma
                                                                                                                               "base_n_lt_n")
                                                                                                                              (("2"
                                                                                                                                (inst?)
                                                                                                                                (("2"
                                                                                                                                  (skeep)
                                                                                                                                  (("2"
                                                                                                                                    (inst?)
                                                                                                                                    (("2"
                                                                                                                                      (assert)
                                                                                                                                      nil
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil)
                                                                                                         ("2"
                                                                                                          (hide
                                                                                                           2)
                                                                                                          (("2"
                                                                                                            (rewrite
                                                                                                             "access_col")
                                                                                                            (("2"
                                                                                                              (expand
                                                                                                               "NSol_vect6k"
                                                                                                               +)
                                                                                                              (("2"
                                                                                                                (rewrite
                                                                                                                 "entry_form_matrix")
                                                                                                                (("2"
                                                                                                                  (hide
                                                                                                                   2)
                                                                                                                  (("2"
                                                                                                                    (skosimp*)
                                                                                                                    (("2"
                                                                                                                      (lemma
                                                                                                                       "base_n_lt_n")
                                                                                                                      (("2"
                                                                                                                        (inst?)
                                                                                                                        (("2"
                                                                                                                          (assert)
                                                                                                                          nil
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil)
                                                                                                       ("2"
                                                                                                        (hide-all-but
                                                                                                         1)
                                                                                                        (("2"
                                                                                                          (skosimp*)
                                                                                                          (("2"
                                                                                                            (assert)
                                                                                                            nil
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil)
                                                                                                 ("2"
                                                                                                  (hide-all-but
                                                                                                   1)
                                                                                                  (("2"
                                                                                                    (skosimp*)
                                                                                                    (("2"
                                                                                                      (lemma
                                                                                                       "base_n_lt_n")
                                                                                                      (("2"
                                                                                                        (inst?)
                                                                                                        (("2"
                                                                                                          (assert)
                                                                                                          nil
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil)
                                                                                                 ("3"
                                                                                                  (hide
                                                                                                   2)
                                                                                                  (("3"
                                                                                                    (hide-all-but
                                                                                                     1)
                                                                                                    (("3"
                                                                                                      (skosimp*)
                                                                                                      (("3"
                                                                                                        (lemma
                                                                                                         "base_n_lt_n")
                                                                                                        (("3"
                                                                                                          (inst?)
                                                                                                          (("3"
                                                                                                            (assert)
                                                                                                            nil
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil)
                                                                                             ("3"
                                                                                              (hide-all-but
                                                                                               1)
                                                                                              (("3"
                                                                                                (skosimp*)
                                                                                                (("3"
                                                                                                  (lemma
                                                                                                   "base_n_lt_n")
                                                                                                  (("3"
                                                                                                    (inst?)
                                                                                                    (("3"
                                                                                                      (assert)
                                                                                                      nil
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil)
                                                                                             ("4"
                                                                                              (hide-all-but
                                                                                               1)
                                                                                              (("4"
                                                                                                (skosimp*)
                                                                                                (("4"
                                                                                                  (lemma
                                                                                                   "base_n_lt_n")
                                                                                                  (("4"
                                                                                                    (inst?)
                                                                                                    (("4"
                                                                                                      (assert)
                                                                                                      nil
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
--> --------------------

--> maximum size reached

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

100%


¤ Dauer der Verarbeitung: 0.25 Sekunden  (vorverarbeitet)  ¤

*© Formatika GbR, Deutschland






Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Anfrage:

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.