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Datei: interval_expr_lnexp.prf   Sprache: Lisp

Original von: PVS©
(elementary_matrices
 (zero_or_nonzero 0
  (zero_or_nonzero-1 nil 3522729752 ("" (grind) 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)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (Matrix type-eq-decl nil matrices nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (zero_row? const-decl "bool" elementary_matrices nil)
    (/= const-decl "boolean" notequal nil)
    (nonzero_row? const-decl "bool" elementary_matrices nil))
   shostak))
 (zero_isnt_nonzero 0
  (zero_isnt_nonzero-1 nil 3522729758 ("" (grind) 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
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    (< const-decl "bool" reals nil)
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    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (Matrix type-eq-decl nil matrices nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (zero_row? const-decl "bool" elementary_matrices nil)
    (/= const-decl "boolean" notequal nil)
    (nonzero_row? const-decl "bool" elementary_matrices nil))
   shostak))
 (nonzero_isnt_zero 0
  (nonzero_isnt_zero-1 nil 3522729771 ("" (grind) 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)
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    (< 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)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (Matrix type-eq-decl nil matrices nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (/= const-decl "boolean" notequal nil)
    (nonzero_row? const-decl "bool" elementary_matrices nil)
    (zero_row? const-decl "bool" elementary_matrices nil))
   shostak))
 (elemM1?_TCC1 0
  (elemM1?_TCC1-1 nil 3492633163 ("" (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)
    (posnat nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (real nonempty-type-from-decl nil reals nil)
    (Matrix type-eq-decl nil matrices nil)
    (square? const-decl "bool" matrices nil)
    (Square type-eq-decl nil matrices 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)
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    (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)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (/= const-decl "boolean" notequal nil)
    (real_lt_is_strict_total_order name-judgement
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    (NOT const-decl "[bool -> bool]" booleans nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (real nonempty-type-from-decl nil reals nil)
    (Matrix type-eq-decl nil matrices nil)
    (square? const-decl "bool" matrices nil)
    (Square type-eq-decl nil matrices 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)
    (< 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)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (/= const-decl "boolean" notequal nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
 (elemM2?_TCC1 0
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    (NOT const-decl "[bool -> bool]" booleans nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (real nonempty-type-from-decl nil reals nil)
    (Matrix type-eq-decl nil matrices nil)
    (square? const-decl "bool" matrices nil)
    (Square type-eq-decl nil matrices 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)
    (< 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)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (/= const-decl "boolean" notequal nil))
   nil))
 (elemM2?_TCC2 0
  (elemM2?_TCC2-1 nil 3492633163 ("" (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)
    (posnat nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (real nonempty-type-from-decl nil reals nil)
    (Matrix type-eq-decl nil matrices nil)
    (square? const-decl "bool" matrices nil)
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    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
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    (< const-decl "bool" reals nil)
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    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (/= const-decl "boolean" notequal nil))
   nil))
 (elemM3?_TCC1 0
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   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
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    (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)
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    (< 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)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_lt_is_strict_total_order name-judgement
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    (/= const-decl "boolean" notequal nil))
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 (elemM3?_TCC2 0
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   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (real nonempty-type-from-decl nil reals nil)
    (Matrix type-eq-decl nil matrices nil)
    (square? const-decl "bool" matrices nil)
    (Square type-eq-decl nil matrices 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)
    (< 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)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (/= const-decl "boolean" notequal nil))
   nil))
 (elemM3?_TCC3 0
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   ((boolean nonempty-type-decl nil booleans nil)
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    (NOT const-decl "[bool -> bool]" booleans nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (real nonempty-type-from-decl nil reals nil)
    (Matrix type-eq-decl nil matrices nil)
    (square? const-decl "bool" matrices nil)
    (Square type-eq-decl nil matrices nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
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    (real_pred const-decl "[number_field -> boolean]" 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)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (/= const-decl "boolean" notequal nil))
   nil))
 (elm1_judgement 0
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    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
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    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (> 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)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (Matrix type-eq-decl nil matrices nil)
    (square? const-decl "bool" matrices nil)
    (Square type-eq-decl nil matrices nil)
    (squareMat? const-decl "bool" matrices nil)
    (SquareMat type-eq-decl nil matrices nil)
    (elemMat1? const-decl "bool" elementary_matrices nil)
    (ElemMat1 type-eq-decl nil elementary_matrices nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (elemM1? const-decl "bool" elementary_matrices nil)
    (elemM1? const-decl "bool" elementary_matrices nil))
   nil))
 (elm2_judgement 0
  (elm2_judgement-1 nil 3500318534 ("" (judgement-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
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    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (> 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)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (Matrix type-eq-decl nil matrices nil)
    (square? const-decl "bool" matrices nil)
    (Square type-eq-decl nil matrices nil)
    (squareMat? const-decl "bool" matrices nil)
    (SquareMat type-eq-decl nil matrices nil)
    (elemMat2? const-decl "bool" elementary_matrices nil)
    (ElemMat2 type-eq-decl nil elementary_matrices nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (/= const-decl "boolean" notequal nil)
    (elemM2? const-decl "bool" elementary_matrices nil)
    (elemM2? const-decl "bool" elementary_matrices nil))
   nil))
 (elm3_judgement 0
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    (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)
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    (> 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)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (Matrix type-eq-decl nil matrices nil)
    (square? const-decl "bool" matrices nil)
    (Square type-eq-decl nil matrices nil)
    (squareMat? const-decl "bool" matrices nil)
    (SquareMat type-eq-decl nil matrices nil)
    (elemMat3? const-decl "bool" elementary_matrices nil)
    (ElemMat3 type-eq-decl nil elementary_matrices nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (/= const-decl "boolean" notequal nil)
    (elemM3? const-decl "bool" elementary_matrices nil)
    (elemM3? const-decl "bool" elementary_matrices nil))
   nil))
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    (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)
    (>= const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (Matrix type-eq-decl nil matrices nil)
    (square? const-decl "bool" matrices nil)
    (Square type-eq-decl nil matrices nil)
    (squareMat? const-decl "bool" matrices nil)
    (SquareMat type-eq-decl nil matrices nil)
    (elemMat? const-decl "bool" elementary_matrices nil)
    (ElemMat type-eq-decl nil elementary_matrices nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (elemMat1? const-decl "bool" elementary_matrices nil)
    (elemMat2? const-decl "bool" elementary_matrices nil)
    (elemMat3? const-decl "bool" elementary_matrices nil)
    (elemM1? const-decl "bool" elementary_matrices nil)
    (elemM1? const-decl "bool" elementary_matrices nil)
    (/= const-decl "boolean" notequal nil)
    (elemM2? const-decl "bool" elementary_matrices nil)
    (elemM2? const-decl "bool" elementary_matrices nil)
    (elemM3? const-decl "bool" elementary_matrices nil)
    (elemM3? const-decl "bool" elementary_matrices nil)
    (elemM? const-decl "bool" elementary_matrices nil))
   nil))
 (elemM1_TCC1 0
  (elemM1_TCC1-1 nil 3492635698
   ("" (skolem-typepred)
    (("" (prop)
      (("1" (grind) nil nil) ("2" (grind) nil nil)
       ("3" (grind)
        (("3" (inst 1 "i!1" "j!1")
          (("3" (skolem-typepred)
            (("3" (prop)
              (("1" (lift-if) (("1" (assert) nil nil)) nil)
               ("2" (lift-if) (("2" (assert) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((square? const-decl "bool" matrices nil)
    (squareMat? const-decl "bool" matrices nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (elemM1? const-decl "bool" elementary_matrices nil)
    (elemMat1? const-decl "bool" elementary_matrices nil)
    (/= const-decl "boolean" notequal nil)
    (below type-eq-decl nil naturalnumbers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (nonneg_int nonempty-type-eq-decl nil integers 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)
    (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)
    (number nonempty-type-decl nil numbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   nil))
 (elemM2_TCC1 0
  (elemM2_TCC1-1 nil 3492635698
   ("" (skolem-typepred)
    (("" (prop)
      (("1" (grind) nil nil) ("2" (grind) nil nil)
       ("3" (expand "elemMat2?")
        (("3" (inst 1 "i!1" "j!1") (("3" (grind) nil nil)) nil)) nil))
      nil))
    nil)
   ((square? const-decl "bool" matrices nil)
    (squareMat? const-decl "bool" matrices nil)
    (elemM2? const-decl "bool" elementary_matrices nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (elemMat2? const-decl "bool" elementary_matrices nil)
    (/= const-decl "boolean" notequal nil)
    (below type-eq-decl nil naturalnumbers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (nonneg_int nonempty-type-eq-decl nil integers 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)
    (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)
    (number nonempty-type-decl nil numbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   nil))
 (elemM3_TCC1 0
  (elemM3_TCC1-1 nil 3492635698
   ("" (skolem-typepred)
    (("" (prop)
      (("1" (grind) nil nil) ("2" (grind) nil nil)
       ("3" (expand "elemMat3?")
        (("3" (inst 1 "i!1") (("3" (grind) nil nil)) nil)) nil))
      nil))
    nil)
   ((square? const-decl "bool" matrices nil)
    (squareMat? const-decl "bool" matrices nil)
    (elemM3? const-decl "bool" elementary_matrices nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (elemMat3? const-decl "bool" elementary_matrices nil)
    (nzreal nonempty-type-eq-decl nil reals nil)
    (/= const-decl "boolean" notequal nil)
    (below type-eq-decl nil naturalnumbers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (nonneg_int nonempty-type-eq-decl nil integers 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)
    (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)
    (number nonempty-type-decl nil numbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   nil))
 (elemM1_invertible 0
  (elemM1_invertible-2 "" 3520306768
   ("" (skolem-typepred)
    (("" (expand "invertible?")
      (("" (expand "elemM1?")
        (("" (skolem-typepred)
          ((""
            (inst 1
             "elemM1(M!1`rows)(i!1, j!1)(-(M!1`matrix(i!1, j!1)))")
            (("1" (prop)
              (("1" (grind) nil nil)
               ("2" (expand "inverse?")
                (("2" (prop)
                  (("1" (expand "elemM1?")
                    (("1" (expand "elemM1")
                      (("1" (expand "*")
                        (("1" (apply-extensionality :hide? t)
                          (("1" (grind) nil nil)
                           ("2" (apply-extensionality :hide? t)
                            (("1" (expand "I")
                              (("1"
                                (lift-if)
                                (("1"
                                  (prop)
                                  (("1"
                                    (lemma
                                     "sigma_middle[below(M!1`cols)]")
                                    (("1"
                                      (inst?
                                       :subst
                                       ("low"
                                        "0"
                                        "high"
                                        "M!1`cols-1"
                                        "i"
                                        "x!1"))
                                      (("1"
                                        (prop)
                                        (("1"
                                          (replace -1 :hide? t)
                                          (("1"
                                            (lemma
                                             "sigma_eq[below(M!1`cols)]")
                                            (("1"
                                              (inst-cp
                                               -1
                                               "LAMBDA (k_1: below(M!1`cols)):
                 (M!1`matrix(x!1, k_1) *
                   IF (k_1 = x!2) THEN 1
                   ELSIF ((k_1 = i!1) AND (x!2 = j!1))
                     THEN -(M!1`matrix(i!1, j!1))
                   ELSE 0
                   ENDIF)"
                                               "LAMBDA (k_1: below(M!1`cols)): 0"
                                               "x!1-1"
                                               "0")
                                              (("1"
                                                (prop)
                                                (("1"
                                                  (replace -1 :hide? t)
                                                  (("1"
                                                    (use
                                                     "sigma_zero[below(M!1`cols)]")
                                                    (("1"
                                                      (replace
                                                       -1
                                                       :hide?
                                                       t)
                                                      (("1"
                                                        (inst
                                                         -1
                                                         "LAMBDA (k_1: below(M!1`cols)):
                 (M!1`matrix(x!1, k_1) *
                   IF (k_1 = x!2) THEN 1
                   ELSIF ((k_1 = i!1) AND (x!2 = j!1))
                     THEN -(M!1`matrix(i!1, j!1))
                   ELSE 0
                   ENDIF)"
                                                         "LAMBDA (k_1: below(M!1`cols)): 0"
                                                         "M!1`cols-1"
                                                         "x!1+1")
                                                        (("1"
                                                          (prop)
                                                          (("1"
                                                            (replace
                                                             -1
                                                             :hide?
                                                             t)
                                                            (("1"
                                                              (use
                                                               "sigma_zero[below(M!1`cols)]")
                                                              (("1"
                                                                (replace
                                                                 -1
                                                                 :hide?
                                                                 t)
                                                                (("1"
                                                                  (assert)
                                                                  (("1"
                                                                    (inst
                                                                     -5
                                                                     "x!1"
                                                                     "x!1")
                                                                    nil
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil)
                                                           ("2"
                                                            (hide 2)
                                                            (("2"
                                                              (skosimp)
                                                              (("2"
                                                                (assert)
                                                                (("2"
                                                                  (inst
                                                                   -5
                                                                   "x!1"
                                                                   "n!1")
                                                                  (("1"
                                                                    (assert)
                                                                    (("1"
                                                                      (prop)
                                                                      (("1"
                                                                        (assert)
                                                                        nil
                                                                        nil)
                                                                       ("2"
                                                                        (assert)
                                                                        (("2"
                                                                          (lift-if)
                                                                          (("2"
                                                                            (assert)
                                                                            nil
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("3"
                                                                        (lift-if)
                                                                        (("3"
                                                                          (assert)
                                                                          nil
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (lift-if)
                                                                    (("2"
                                                                      (assert)
                                                                      nil
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil)
                                                         ("2"
                                                          (hide -5 2)
                                                          (("2"
                                                            (grind)
                                                            nil
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (hide 2)
                                                  (("2"
                                                    (hide -1)
                                                    (("2"
                                                      (skolem-typepred)
                                                      (("2"
                                                        (inst
                                                         -7
                                                         "x!1"
                                                         "n!1")
                                                        (("2"
                                                          (assert)
                                                          (("2"
                                                            (assert)
                                                            (("2"
                                                              (prop)
                                                              (("1"
                                                                (lift-if)
                                                                (("1"
                                                                  (assert)
                                                                  nil
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (lift-if)
                                                                (("2"
                                                                  (assert)
                                                                  nil
                                                                  nil))
                                                                nil)
                                                               ("3"
                                                                (lift-if)
                                                                (("3"
                                                                  (assert)
                                                                  nil
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)
                                               ("2"
                                                (hide -5 2)
                                                (("2" (grind) nil nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (hide -5 2)
                                          (("2" (grind) nil nil))
                                          nil)
                                         ("3"
                                          (hide -5 2)
                                          (("3" (grind) nil nil))
                                          nil))
                                        nil)
                                       ("2"
                                        (hide -5 2)
                                        (("2" (grind) nil nil))
                                        nil)
                                       ("3"
                                        (hide -5 2)
                                        (("3" (grind) nil nil))
                                        nil)
                                       ("4"
                                        (hide -6 2)
                                        (("4" (grind) nil nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (hide -5 2)
                                      (("2" (grind) nil nil))
                                      nil))
                                    nil)
                                   ("2"
                                    (case-replace "x!1 = i!1")
                                    (("1"
                                      (inst -5 "i!1" _)
                                      (("1"
                                        (case "x!2 = j!1")
                                        (("1"
                                          (replace -1)
                                          (("1"
                                            (lemma
                                             "sigma_middle[below(M!1`cols)]")
                                            (("1"
                                              (inst?
                                               :subst
                                               ("low"
                                                "0"
                                                "high"
                                                "M!1`cols-1"
                                                "i"
                                                "min(i!1,j!1)"))
                                              (("1"
                                                (prop)
                                                (("1"
                                                  (replace -1 :hide? t)
                                                  (("1"
                                                    (lemma
                                                     "sigma_middle[below(M!1`cols)]")
                                                    (("1"
                                                      (inst?
                                                       :subst
                                                       ("low"
                                                        "min(i!1,j!1)+1"
                                                        "high"
                                                        "M!1`cols-1"
                                                        "i"
                                                        "max(i!1, j!1)"))
                                                      (("1"
                                                        (prop)
                                                        (("1"
                                                          (replace
                                                           -1
                                                           :hide?
                                                           t)
                                                          (("1"
                                                            (lemma
                                                             "sigma_eq[below(M!1`cols)]")
                                                            (("1"
                                                              (inst-cp
                                                               -1
                                                               "LAMBDA (k_1: below(M!1`cols)):
                    (M!1`matrix(i!1, k_1) *
                      IF (k_1 = j!1) THEN 1
                      ELSIF (k_1 = i!1) THEN -(M!1`matrix(i!1, j!1))
                      ELSE 0
                      ENDIF)"
                                                               "LAMBDA (k_1: below(M!1`cols)): 0"
                                                               "min(i!1,j!1)-1"
                                                               "0")
                                                              (("1"
                                                                (prop)
                                                                (("1"
                                                                  (replace
                                                                   -1
                                                                   :hide?
                                                                   t)
                                                                  (("1"
                                                                    (use
                                                                     "sigma_zero[below(M!1`cols)]")
                                                                    (("1"
                                                                      (replace
                                                                       -1
                                                                       :hide?
                                                                       t)
                                                                      (("1"
                                                                        (assert)
                                                                        (("1"
                                                                          (inst-cp
                                                                           -1
                                                                           "LAMBDA (k_1: below(M!1`cols)):
                    (M!1`matrix(i!1, k_1) *
                      IF (k_1 = j!1) THEN 1
                      ELSIF (k_1 = i!1) THEN -(M!1`matrix(i!1, j!1))
                      ELSE 0
                      ENDIF)"
                                                                           "LAMBDA (k_1: below(M!1`cols)): 0"
                                                                           "max(i!1,j!1)-1"
                                                                           "min(i!1,j!1)+1")
                                                                          (("1"
                                                                            (prop)
                                                                            (("1"
                                                                              (replace
                                                                               -1
                                                                               :hide?
                                                                               t)
                                                                              (("1"
                                                                                (use
                                                                                 "sigma_zero[below(M!1`cols)]")
                                                                                (("1"
                                                                                  (replace
                                                                                   -1
                                                                                   :hide?
                                                                                   t)
                                                                                  (("1"
                                                                                    (assert)
                                                                                    (("1"
                                                                                      (inst
                                                                                       -1
                                                                                       "LAMBDA (k_1: below(M!1`cols)):
                    (M!1`matrix(i!1, k_1) *
                      IF (k_1 = j!1) THEN 1
                      ELSIF (k_1 = i!1) THEN -(M!1`matrix(i!1, j!1))
                      ELSE 0
                      ENDIF)"
                                                                                       "LAMBDA (k_1: below(M!1`cols)): 0"
                                                                                       "M!1`cols-1"
                                                                                       "max(i!1,j!1)+1")
                                                                                      (("1"
                                                                                        (prop)
                                                                                        (("1"
                                                                                          (replace
                                                                                           -1
                                                                                           :hide?
                                                                                           t)
                                                                                          (("1"
                                                                                            (use
                                                                                             "sigma_zero[below(M!1`cols)]")
                                                                                            (("1"
                                                                                              (replace
                                                                                               -1
                                                                                               :hide?
                                                                                               t)
                                                                                              (("1"
                                                                                                (assert)
                                                                                                (("1"
                                                                                                  (expand
                                                                                                   "min")
                                                                                                  (("1"
                                                                                                    (lift-if)
                                                                                                    (("1"
                                                                                                      (prop)
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "max")
                                                                                                        (("1"
                                                                                                          (assert)
                                                                                                          (("1"
                                                                                                            (inst
                                                                                                             -7
                                                                                                             "i!1")
                                                                                                            (("1"
                                                                                                              (assert)
                                                                                                              nil
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil)
                                                                                                       ("2"
                                                                                                        (expand
                                                                                                         "max")
                                                                                                        (("2"
                                                                                                          (assert)
                                                                                                          (("2"
                                                                                                            (assert)
                                                                                                            (("2"
                                                                                                              (inst
                                                                                                               -6
                                                                                                               "i!1")
                                                                                                              nil
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil)
                                                                                         ("2"
                                                                                          (hide
                                                                                           3)
                                                                                          (("2"
                                                                                            (skolem-typepred)
                                                                                            (("2"
                                                                                              (expand
                                                                                               "max")
                                                                                              (("2"
                                                                                                (lift-if)
                                                                                                (("2"
                                                                                                  (assert)
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil)
                                                                                       ("2"
                                                                                        (hide
                                                                                         -6
                                                                                         3)
                                                                                        (("2"
                                                                                          (flatten)
                                                                                          (("2"
                                                                                            (inst
                                                                                             2
                                                                                             "max(i!1,j!1)")
                                                                                            (("1"
                                                                                              (grind)
                                                                                              nil
                                                                                              nil)
                                                                                             ("2"
                                                                                              (grind)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil)
                                                                                       ("3"
                                                                                        (hide
                                                                                         -6
                                                                                         3)
                                                                                        (("3"
                                                                                          (grind)
                                                                                          nil
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil)
                                                                             ("2"
                                                                              (hide
                                                                               3)
                                                                              (("2"
                                                                                (hide
                                                                                 -1)
                                                                                (("2"
                                                                                  (skolem-typepred)
                                                                                  (("2"
                                                                                    (expand
                                                                                     "min")
                                                                                    (("2"
                                                                                      (lift-if)
                                                                                      (("2"
                                                                                        (bddsimp
                                                                                         -1)
                                                                                        (("1"
                                                                                          (assert)
                                                                                          (("1"
                                                                                            (expand
                                                                                             "max")
                                                                                            (("1"
                                                                                              (assert)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil)
                                                                                         ("2"
                                                                                          (expand
                                                                                           "max")
                                                                                          (("2"
                                                                                            (assert)
                                                                                            nil
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (hide
                                                                             -6
                                                                             3)
                                                                            (("2"
                                                                              (flatten)
                                                                              (("2"
                                                                                (inst
                                                                                 2
                                                                                 "min(i!1,j!1)")
                                                                                (("1"
                                                                                  (grind)
--> --------------------

--> maximum size reached

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

¤ Dauer der Verarbeitung: 0.25 Sekunden  (vorverarbeitet)  ¤



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