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Datei: pointwise_orders_aux.prf   Sprache: Lisp

Original von: PVS©

(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)
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        (("" (lemma "columns_form_matrix")
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        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)
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    (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))
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                        (("2" (assert)
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                                (expand "^")
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                  nil))
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      nil))
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    (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)
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    (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/")
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     "(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)
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    (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
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   ("" (skosimp*)
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    (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)
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    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
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    (rational_pred const-decl "[real -> boolean]" rationals nil)
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    (number_field_pred const-decl "[number -> boolean]" number_fields
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    (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)
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    (integer_pred const-decl "[rational -> boolean]" integers nil)
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    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
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    (/= 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])"
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    (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)
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    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
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    (rational_pred const-decl "[real -> boolean]" rationals nil)
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    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
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    (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))
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   ("" (skeep)
    (("" (rewrite "rows_form_matrix")
      (("" (assert)
        (("" (lemma "columns_form_matrix")
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        nil))
      nil))
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   ((nnint_plus_posint_is_posint application-judgement "posint"
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    (integer_pred const-decl "[rational -> boolean]" integers nil)
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    (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
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    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/")
    (every adt-def-decl "boolean" list_adt nil))
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  (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
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    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/")
    (every adt-def-decl "boolean" list_adt nil))
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    (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))
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   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
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    (id const-decl "(bijective?[T, T])" identity nil)
    (TRUE const-decl "bool" booleans nil))
   nil))
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   ((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))
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  (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))
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                                                                                                              (("2"
                                                                                                                (rewrite
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                                                                                                                  (hide
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                                                                                                                  (("2"
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--> --------------------

--> maximum size reached

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

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