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Datei: clock_shift.prf Sprache: Lisp

Original von: PVS^©

(clock_shift
(offset_left_edge 0
  (offset_left_edge-1 nil 3403541539
   ("" (skosimp*)
    (("" (expand "offset")
      (("" (expand "clock_edge?")
        (("" (skosimp*)
          (("" (replace -1 :hide? t)
            (("" (rewrite "Clock_rewrite")
              (("" (use "drift_left") (("" (assert) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((offset const-decl "real" clock_shift nil)
    (Clock_rewrite formula-decl nil inverse_clocks 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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (rate const-decl "posreal" physical_clocks nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (good_clock nonempty-type-eq-decl nil physical_clocks nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (N formal-const-decl "posnat" clock_shift nil)
    (below type-eq-decl nil naturalnumbers 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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (rho formal-const-decl "nonneg_real" clock_shift nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (integer nonempty-type-from-decl nil integers nil)
    (drift_left formula-decl nil physical_clocks nil)
    (clock_edge? const-decl "bool" physical_clocks nil))
   nil))
(offset_left 0
  (offset_left-1 nil 3356340049
   ("" (skosimp*)
    (("" (expand "offset")
      (("" (use "Clock_upper")
        (("" (lemma "drift_right_nat")
          (("" (inst?)
            (("" (lemma "drift_left_nat")
              (("" (inst - _ "X!1" "c!1(n!1)")
                (("" (inst?) (("" (assert) nil nil)) nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((offset const-decl "real" clock_shift nil)
    (drift_right_nat formula-decl nil physical_clocks nil)
    (drift_left_nat formula-decl nil physical_clocks nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (C const-decl "int" inverse_clocks nil)
    (odd_minus_odd_is_even application-judgement "even_int" integers
     nil)
    (nnreal_div_posreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (int_minus_int_is_int application-judgement "int" integers 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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (rate const-decl "posreal" physical_clocks nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (good_clock nonempty-type-eq-decl nil physical_clocks nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (N formal-const-decl "posnat" clock_shift nil)
    (below type-eq-decl nil naturalnumbers nil)
    (rho formal-const-decl "nonneg_real" clock_shift nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (Clock_upper formula-decl nil inverse_clocks nil))
   shostak))
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  (offset_right_edge-1 nil 3403542544
   ("" (skosimp*)
    (("" (expand "offset")
      (("" (expand "clock_edge?")
        (("" (skosimp*)
          (("" (replace -1 :hide? t)
            (("" (rewrite "Clock_rewrite")
              (("" (use "drift_right") (("" (assert) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((offset const-decl "real" clock_shift nil)
    (Clock_rewrite formula-decl nil inverse_clocks 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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (rate const-decl "posreal" physical_clocks nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (good_clock nonempty-type-eq-decl nil physical_clocks nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (N formal-const-decl "posnat" clock_shift nil)
    (below type-eq-decl nil naturalnumbers 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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (rho formal-const-decl "nonneg_real" clock_shift nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (integer nonempty-type-from-decl nil integers nil)
    (drift_right formula-decl nil physical_clocks nil)
    (clock_edge? const-decl "bool" physical_clocks nil))
   nil))
(offset_right 0
  (offset_right-2 nil 3356340177
   ("" (skosimp*)
    (("" (expand "offset")
      (("" (use "Clock_lower")
        (("" (lemma "drift_right")
          ((""
            (invoke (inst - "%1" "%2" "c!1(n!1)") (! -2 l 1)
             (! 1 l 1 1))
            (("" (assert) nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((offset const-decl "real" clock_shift nil)
    (drift_right formula-decl nil physical_clocks nil)
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (C const-decl "int" inverse_clocks 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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (rate const-decl "posreal" physical_clocks nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (good_clock nonempty-type-eq-decl nil physical_clocks nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (N formal-const-decl "posnat" clock_shift nil)
    (below type-eq-decl nil naturalnumbers nil)
    (rho formal-const-decl "nonneg_real" clock_shift nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (Clock_lower formula-decl nil inverse_clocks nil))
   nil)
  (offset_right-1 nil 3356340147
   ("" (induct "k")
    (("1" (skosimp*) (("1" (expand "sigma") (("1" (assert) nil)))))
     ("2" (skosimp*)
      (("2" (rewrite "sigma_last")
        (("2" (inst?)
          (("2" (inst?)
            (("2" (inst?)
              (("2" (inst?)
                (("2" (prop)
                  (("1" (rewrite "+")
                    (("1" (move-terms 1 l (2 3))
                      (("1"
                        (invoke
                         (then (case "%1 <= %2") (assert) (hide -1 2))
                         (! -1 r) (! 1 r))
                        (("1" (expand* "*" "synch_protocol" "v_min")
                          (("1" (inst?)
                            (("1" (assert)
                              (("1"
                                (replace -1 :hide? t)
                                (("1"
                                  (isolate 1 r 2)
                                  (("1"
                                    (expand*
                                     "clock_relation?"
                                     "nominal"
                                     "epsilon_lower")
                                    (("1"
                                      (inst?)
                                      (("1"
                                        (expand*
                                         "majority_synch?"
                                         "majority?"
                                         "correct_denotation"
                                         "conforms"
                                         "received")
                                        (("1"
                                          (inst?)
                                          (("1"
                                            (assert)
                                            (("1"
                                              (use
                                               "lower_synch_validity[source_error(j!1+j!2), rho, min_latency(j!1 + j!2), var_latency(j!1 + j!2), stage(j!1 + j!2), stage(1 + j!1 + j!2)]")
                                              (("1"
                                                (expand
                                                 "majority_synch?")
                                                (("1"
                                                  (propax)
                                                  nil)))))))))))))))))))))))))))))))
                   ("2" (hide-all-but (-1 1))
                    (("2" (expand "synch_protocol")
                      (("2" (skosimp*)
                        (("2" (inst?) (("2" (assert) nil)))))))))
                   ("3" (hide-all-but (-2 1))
                    (("3" (expand "majority_synch?")
                      (("3" (expand "majority?")
                        (("3" (skosimp*)
                          (("3" (inst?)
                            (("3" (assert)
                              nil))))))))))))))))))))))))))
    nil)
   nil nil))
(offset_zero 0
  (offset_zero-1 nil 3357289330
   ("" (skosimp*)
    (("" (apply-extensionality :hide? t)
      (("" (expand "all_clock_edge?")
        (("" (inst?)
          (("" (expand "clock_edge?")
            (("" (skosimp*)
              (("" (expand "offset")
                (("" (replace -1 :hide? t)
                  (("" (rewrite "Clock_rewrite") nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    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)
    (< const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (N formal-const-decl "posnat" clock_shift nil)
    (below type-eq-decl nil naturalnumbers nil)
    (offset const-decl "real" clock_shift nil)
    (integer nonempty-type-from-decl nil integers nil)
    (good_clock nonempty-type-eq-decl nil physical_clocks nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (rate const-decl "posreal" physical_clocks nil)
    (rho formal-const-decl "nonneg_real" clock_shift nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (Clock_rewrite formula-decl nil inverse_clocks nil)
    (clock_edge? const-decl "bool" physical_clocks nil)
    (all_clock_edge? const-decl "bool" clock_shift nil))
   shostak))
(offset_drift 0
  (offset_drift-1 nil 3356340216
   ("" (skosimp*)
    (("" (expand "offset")
      (("" (use "relative_drift")
        (("" (assert)
          (("" (move-terms 1 r 3)
            (("" (move-terms -1 r 3)
              ((""
                (invoke (then (case "%1 < %2") (assert) (hide -1 2))
                 (! -1 r) (! 1 r))
                (("" (use "Clock_lower")
                  (("" (lemma "Clock_upper")
                    (("" (inst - "c!1(n1!1)" "local_event!1(n1!1)")
                      (("" (use "drift_right_nat")
                        (("" (assert) nil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((offset const-decl "real" clock_shift nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (Clock_lower formula-decl nil inverse_clocks nil)
    (posreal_times_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (drift_right_nat formula-decl nil physical_clocks nil)
    (Clock_upper formula-decl nil inverse_clocks nil)
    (IFF const-decl "[bool, bool -> bool]" booleans nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (drift const-decl "nonneg_real" physical_clocks nil)
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (real_minus_real_is_real application-judgement "real" 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)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (rate const-decl "posreal" physical_clocks nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (good_clock nonempty-type-eq-decl nil physical_clocks nil)
    (C const-decl "int" inverse_clocks nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (N formal-const-decl "posnat" clock_shift nil)
    (below type-eq-decl nil naturalnumbers nil)
    (rho formal-const-decl "nonneg_real" clock_shift nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (relative_drift formula-decl nil physical_clocks nil))
   shostak))
(offset_nondecreasing 0
  (offset_nondecreasing-1 nil 3403617770
   ("" (skosimp*)
    (("" (expand "offset")
      (("" (rewrite "clock_nondecreasing")
        (("" (isolate 1 r 1)
          (("" (assert) (("" (rewrite "Clock_nondecreasing") nil nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((offset const-decl "real" clock_shift nil)
    (IFF const-decl "[bool, bool -> bool]" booleans nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (Clock_nondecreasing formula-decl nil inverse_clocks nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (rho formal-const-decl "nonneg_real" clock_shift nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (integer nonempty-type-from-decl nil integers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N formal-const-decl "posnat" clock_shift nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (< const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (C const-decl "int" inverse_clocks nil)
    (good_clock nonempty-type-eq-decl nil physical_clocks nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (rate const-decl "posreal" physical_clocks nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals 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 "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields 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)
    (clock_nondecreasing formula-decl nil physical_clocks nil)
    (int_plus_int_is_int application-judgement "int" integers nil))
   shostak))
(offset_drift_edge 0
  (offset_drift_edge-1 nil 3403544266
   ("" (skosimp*)
    (("" (expand "offset")
      (("" (expand "clock_edge?")
        (("" (skosimp*)
          (("" (replace*)
            (("" (hide -1 -2)
              (("" (rewrite "Clock_rewrite")
                (("" (rewrite "Clock_rewrite")
                  (("" (use "relative_drift") (("" (assert) nil nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((offset const-decl "real" clock_shift nil)
    (relative_drift formula-decl nil physical_clocks nil)
    (rho formal-const-decl "nonneg_real" clock_shift nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N formal-const-decl "posnat" clock_shift nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (< const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (good_clock nonempty-type-eq-decl nil physical_clocks nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (rate const-decl "posreal" physical_clocks nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" 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)
    (Clock_rewrite formula-decl nil inverse_clocks nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (nnreal_times_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (clock_edge? const-decl "bool" physical_clocks nil))
   nil))
(double_offset 0
  (double_offset-1 nil 3356340325
   ("" (skosimp*)
    (("" (apply-extensionality :hide? t)
      (("" (expand "offset")
        (("" (assert)
          (("" (rewrite "Clock_rewrite") (("" (assert) nil nil)) nil))
          nil))
        nil))
      nil))
    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)
    (< const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (N formal-const-decl "posnat" clock_shift nil)
    (below type-eq-decl nil naturalnumbers nil)
    (offset const-decl "real" clock_shift nil)
    (integer nonempty-type-from-decl nil integers nil)
    (good_clock nonempty-type-eq-decl nil physical_clocks nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (rate const-decl "posreal" physical_clocks nil)
    (rho formal-const-decl "nonneg_real" clock_shift nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (C const-decl "int" inverse_clocks nil)
    (Clock_rewrite formula-decl nil inverse_clocks nil))
   shostak))
(offset_same 0
  (offset_same-1 nil 3356422620
   ("" (skosimp*)
    (("" (prop)
      (("1" (lemma "congruence[below(N), real]")
        (("1" (inst?)
          (("1" (apply-extensionality :hide? t)
            (("1" (inst - "x!1" "x!1")
              (("1" (hide -2)
                (("1" (expand "offset")
                  (("1" (expand "same_edges?")
                    (("1" (inst?)
                      (("1" (expand "offset_clocks?")
                        (("1" (skosimp*)
                          (("1" (invoke (inst-cp - "%1") (! -1 l 1))
                            (("1" (invoke (inst - "%1") (! 1 l 1))
                              (("1"
                                (replace*)
                                (("1"
                                  (hide -1 -2)
                                  (("1"
                                    (assert)
                                    (("1"
                                      (forward-chain "clock_eq_arg")
                                      (("1" (assert) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (lemma "double_offset")
        (("2" (inst-cp - "T1!1" "T2!1" "c1!1" "le1!1")
          (("2" (inst - "T1!1" "T2!1" "c2!1" "le2!1")
            (("2" (assert)
              (("2" (replace -1 :dir rl :hide? t)
                (("2" (replace -1 :dir rl :hide? t)
                  (("2" (replace -1 :dir rl :hide? t)
                    (("2" (expand "offset")
                      (("2" (apply-extensionality :hide? t)
                        (("2" (rewrite "Clock_rewrite")
                          (("2" (expand "same_edges?")
                            (("2" (inst?)
                              (("2"
                                (expand "offset_clocks?")
                                (("2"
                                  (skosimp*)
                                  (("2"
                                    (invoke
                                     (inst-cp - "%1")
                                     (! 1 r 1 1 1 1))
                                    (("2"
                                      (replace*)
                                      (("2"
                                        (rewrite "Clock_rewrite")
                                        (("2"
                                          (hide -2)
                                          (("2"
                                            (inst?)
                                            (("2" (assert) nil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((int_plus_int_is_int application-judgement "int" integers nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (rho formal-const-decl "nonneg_real" clock_shift nil)
    (rate const-decl "posreal" physical_clocks nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (good_clock nonempty-type-eq-decl nil physical_clocks nil)
    (integer nonempty-type-from-decl nil integers nil)
    (offset const-decl "real" clock_shift nil)
    (clock_eq_arg formula-decl nil physical_clocks nil)
    (C const-decl "int" inverse_clocks nil)
    (offset_clocks? const-decl "bool" physical_clocks nil)
    (same_edges? const-decl "bool" clock_shift nil)
    (congruence formula-decl nil functions 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)
    (< const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (N formal-const-decl "posnat" clock_shift nil)
    (below type-eq-decl nil naturalnumbers nil)
    (Clock_rewrite formula-decl nil inverse_clocks nil)
    (double_offset formula-decl nil clock_shift nil))
   shostak))
(offset_same2 0
  (offset_same2-1 nil 3356696194
   ("" (skosimp*)
    (("" (lemma "offset_same")
      (("" (inst - "T1!1" 0 "c1!1" "c2!1" "le1!1" "le2!1")
        (("" (assert)
          (("" (replace -1 :hide? t)
            (("" (rewrite "offset_zero")
              (("" (rewrite "offset_zero") (("" (assert) nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((offset_same formula-decl nil clock_shift nil)
    (offset_zero formula-decl nil clock_shift nil)
    (good_clock nonempty-type-eq-decl nil physical_clocks nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (rate const-decl "posreal" physical_clocks nil)
    (rho formal-const-decl "nonneg_real" clock_shift nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (below type-eq-decl nil naturalnumbers nil)
    (N formal-const-decl "posnat" clock_shift nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (< const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer nonempty-type-from-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))
   shostak)))

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