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Datei: deriv_domain_def.prf Sprache: Lisp

Original von: PVS^©

(deriv_domain_def
(connected_deriv_domain 0
  (connected_deriv_domain-1 nil 3472397987
   ("" (flatten)
    (("" (expand "connected?")
      (("" (expand "not_one_element?")
        (("" (expand "deriv_domain?")
          (("" (skolem!)
            (("" (inst -2 "x!1")
              (("" (skosimp*)
                (("" (case "abs(y!1 - x!1) < e!1")
                  (("1" (inst? 2) (("1" (assert) nil nil)) nil)
                   ("2"
                    (inst 3
                     "if x!1 < y!1 then e!1/2 else -e!1/2 endif")
                    (("1" (grind) nil nil)
                     ("2" (flatten)
                      (("2" (inst - "y!1" "x!1" "_")
                        (("2" (grind) nil nil)) nil))
                      nil)
                     ("3" (inst - "x!1" "y!1" "_")
                      (("3" (inst?)
                        (("3" (flatten) (("3" (grind) nil nil)) nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((connected? const-decl "bool" deriv_domain_def nil)
    (deriv_domain? const-decl "bool" deriv_domain_def 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)
    (T_pred const-decl "[real -> boolean]" deriv_domain_def nil)
    (T formal-subtype-decl nil deriv_domain_def nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (x!1 skolem-const-decl "T" deriv_domain_def nil)
    (y!1 skolem-const-decl "T" deriv_domain_def nil)
    (/= const-decl "boolean" notequal nil)
    (nzreal nonempty-type-eq-decl nil reals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (e!1 skolem-const-decl "posreal" deriv_domain_def nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (minus_nzreal_is_nzreal application-judgement "nzreal" real_types
     nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (not_one_element? const-decl "bool" deriv_domain_def nil))
   nil))
(del_neigh_all_lem 0
  (del_neigh_all_lem-1 nil 3474887925
   ("" (flatten)
    (("" (expand "deriv_domain?")
      (("" (skosimp*)
        (("" (expand "del_neigh_all?")
          (("" (inst - "x!1")
            (("" (skosimp*)
              (("" (inst - "x!1 + min(del!1,e!1)/2")
                (("" (split -1)
                  (("1" (inst + "min(del!1, e!1) / 2")
                    (("1" (grind) nil nil) ("2" (grind) nil nil)) nil)
                   ("2" (grind) nil nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((deriv_domain? const-decl "bool" deriv_domain_def nil)
    (del_neigh_all? const-decl "bool" deriv_domain_def nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (nonzero_abs_is_pos application-judgement "{y: posreal | y >= x}"
     real_defs 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)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (nzreal nonempty-type-eq-decl nil reals nil)
    (x!1 skolem-const-decl "T" deriv_domain_def nil)
    (e!1 skolem-const-decl "posreal" deriv_domain_def nil)
    (del!1 skolem-const-decl "posreal" deriv_domain_def nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (posreal_min application-judgement
     "{z: posreal | z <= x AND z <= y}" real_defs nil)
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (T formal-subtype-decl nil deriv_domain_def nil)
    (T_pred const-decl "[real -> boolean]" deriv_domain_def 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_minus_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil))
   nil)))

¤ Dauer der Verarbeitung: 0.1 Sekunden (vorverarbeitet) ¤

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