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Datei: vect_fun_ops.prf Sprache: Lisp

Original von: PVS^©

(max (cauchy_max_TCC1 0
      (cauchy_max_TCC1-1 nil 3251054936
       ("" (expand "cauchy_real?")
        (("" (skosimp*)
          (("" (typepred "cx!1")
            (("" (typepred "cy!1")
              (("" (expand "cauchy_real?")
                (("" (skosimp*)
                  (("" (inst + "max(x!2,x!1)")
                    (("" (expand "cauchy_prop")
                      (("" (skosimp*)
                        (("" (lemma "expt_pos" ("px" "2" "i" "p!1"))
                          (("" (inst - "p!1")
                            (("" (inst - "p!1")
                              ((""
                                (case "cx!1(p!1) < cy!1(p!1)")
                                (("1"
                                  (lemma
                                   "both_sides_times_pos_lt1"
                                   ("x" "x!1" "y" "x!2" "pz" "2^p!1"))
                                  (("1" (grind) nil nil))
                                  nil)
                                 ("2"
                                  (lemma
                                   "both_sides_times_pos_lt1"
                                   ("x" "x!2" "y" "x!1" "pz" "2^p!1"))
                                  (("2" (grind) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ((posint_exp application-judgement "posint" exponentiation nil)
        (int_max application-judgement "{k: int | i <= k AND j <= k}"
         real_defs nil)
        (rat_max application-judgement "{s: rat | s >= q AND s >= r}"
         real_defs nil)
        (cauchy_prop const-decl "bool" cauchy nil)
        (expt_pos formula-decl nil exponentiation nil)
        (nonneg_real nonempty-type-eq-decl nil real_types nil)
        (> const-decl "bool" reals nil)
        (posreal nonempty-type-eq-decl nil real_types nil)
        (both_sides_times_pos_lt1 formula-decl nil real_props nil)
        (OR const-decl "[bool, bool -> bool]" booleans nil)
        (/= const-decl "boolean" notequal nil)
        (^ const-decl "real" exponentiation nil)
        (real_minus_real_is_real application-judgement "real" reals
         nil)
        (int_plus_int_is_int application-judgement "int" integers nil)
        (int_minus_int_is_int application-judgement "int" integers nil)
        (real_gt_is_strict_total_order name-judgement
         "(strict_total_order?[real])" real_props nil)
        (real_ge_is_total_order name-judgement "(total_order?[real])"
         real_props nil)
        (posrat_div_posrat_is_posrat application-judgement "posrat"
         rationals nil)
        (posnat_expt application-judgement "posnat" exponentiation nil)
        (real_times_real_is_real application-judgement "real" reals
         nil)
        (real_lt_is_strict_total_order name-judgement
         "(strict_total_order?[real])" real_props nil)
        (< const-decl "bool" reals nil)
        (AND const-decl "[bool, bool -> bool]" booleans nil)
        (max const-decl "{p: real | p >= m AND p >= n}" real_defs 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)
        (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)
        (cauchy_real nonempty-type-eq-decl nil cauchy nil)
        (cauchy_real? const-decl "bool" cauchy nil))
       shostak))
     (max_lemma 0
      (max_lemma-1 nil 3251054748
       ("" (expand "cauchy_max")
        (("" (expand "cauchy_prop")
          (("" (skosimp*)
            (("" (inst - "p!1")
              (("" (inst - "p!1")
                (("" (lemma "expt_pos" ("px" "2" "i" "p!1"))
                  (("" (case "cx!1(p!1) < cy!1(p!1)")
                    (("1"
                      (lemma "both_sides_times_pos_lt1"
                       ("x" "y!1" "y" "x!1" "pz" "2^p!1"))
                      (("1" (grind) nil nil)) nil)
                     ("2"
                      (lemma "both_sides_times_pos_lt1"
                       ("x" "x!1" "y" "y!1" "pz" "2^p!1"))
                      (("2" (grind) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ((posint_exp application-judgement "posint" exponentiation nil)
        (int_max application-judgement "{k: int | i <= k AND j <= k}"
         real_defs nil)
        (rat_max application-judgement "{s: rat | s >= q AND s >= r}"
         real_defs nil)
        (cauchy_prop const-decl "bool" cauchy nil)
        (number nonempty-type-decl nil numbers nil)
        (boolean nonempty-type-decl nil booleans nil)
        (number_field_pred const-decl "[number -> boolean]"
         number_fields nil)
        (number_field nonempty-type-from-decl nil number_fields nil)
        (real_pred const-decl "[number_field -> boolean]" reals nil)
        (real nonempty-type-from-decl nil reals nil)
        (rational_pred const-decl "[real -> boolean]" rationals nil)
        (rational nonempty-type-from-decl nil rationals nil)
        (integer_pred const-decl "[rational -> boolean]" integers nil)
        (int nonempty-type-eq-decl nil integers nil)
        (bool nonempty-type-eq-decl nil booleans nil)
        (>= const-decl "bool" reals nil)
        (nat nonempty-type-eq-decl nil naturalnumbers nil)
        (expt_pos formula-decl nil exponentiation nil)
        (nonneg_real nonempty-type-eq-decl nil real_types nil)
        (> const-decl "bool" reals nil)
        (posreal nonempty-type-eq-decl nil real_types nil)
        (both_sides_times_pos_lt1 formula-decl nil real_props nil)
        (OR const-decl "[bool, bool -> bool]" booleans nil)
        (/= const-decl "boolean" notequal nil)
        (^ const-decl "real" exponentiation nil)
        (real_minus_real_is_real application-judgement "real" reals
         nil)
        (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
        (int_plus_int_is_int application-judgement "int" integers nil)
        (int_minus_int_is_int application-judgement "int" integers nil)
        (real_gt_is_strict_total_order name-judgement
         "(strict_total_order?[real])" real_props nil)
        (real_ge_is_total_order name-judgement "(total_order?[real])"
         real_props nil)
        (posrat_div_posrat_is_posrat application-judgement "posrat"
         rationals nil)
        (posnat_expt application-judgement "posnat" exponentiation nil)
        (real_times_real_is_real application-judgement "real" reals
         nil)
        (real_lt_is_strict_total_order name-judgement
         "(strict_total_order?[real])" real_props nil)
        (cauchy_real nonempty-type-eq-decl nil cauchy nil)
        (cauchy_real? const-decl "bool" cauchy nil)
        (< const-decl "bool" reals nil)
        (cauchy_max const-decl "cauchy_real" max nil))
       shostak)))

¤ Dauer der Verarbeitung: 0.3 Sekunden (vorverarbeitet) ¤

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