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Datei: Eulerian.prf Sprache: Lisp

Original von: PVS^©

(Eulerian
(no_repeat_subseq?_TCC1 0
  (no_repeat_subseq?_TCC1-1 nil 3561330533 ("" (subtype-tcc) nil nil)
   nil nil))
(no_repeat_subseq?_TCC2 0
  (no_repeat_subseq?_TCC2-1 nil 3561330533 ("" (subtype-tcc) nil nil)
   nil nil))
(no_repeat_subseq?_TCC3 0
  (no_repeat_subseq?_TCC3-1 nil 3561330533 ("" (subtype-tcc) nil nil)
   nil nil))
(no_repeat_subseq?_TCC4 0
  (no_repeat_subseq?_TCC4-1 nil 3561330533 ("" (subtype-tcc) nil nil)
   nil nil))
(cycle_is_pre_Eulerian_circuit 0
  (cycle_is_pre_Eulerian_circuit-1 nil 3564331623
   ("" (skeep)
    (("" (expand "cycle?")
      (("" (expand "pre_Eulerian_circuit?")
        (("" (flatten)
          (("" (assert)
            (("" (expand "pre_Eulerian_walk?")
              (("" (expand "circuit?")
                (("" (expand "pre_circuit?")
                  (("" (flatten)
                    (("" (assert)
                      (("" (expand "no_repeat_subseq?")
                        (("" (expand "finseq_appl")
                          (("" (skeep)
                            (("" (inst -4 "i" "j")
                              (("" (assert) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((cycle? const-decl "bool" cycles nil)
    (pre_Eulerian_walk? const-decl "bool" Eulerian nil)
    (pre_circuit? const-decl "bool" circuits nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     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)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (below type-eq-decl nil nat_types nil)
    (T formal-type-decl nil Eulerian nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (> const-decl "bool" reals nil)
    (prewalk type-eq-decl nil walks nil)
    (below type-eq-decl nil naturalnumbers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (no_repeat_subseq? const-decl "bool" Eulerian nil)
    (circuit? const-decl "bool" circuits nil)
    (pre_Eulerian_circuit? const-decl "bool" Eulerian nil))
   shostak))
(pre_Eulerian_circuit_is_a_circuit 0
  (pre_Eulerian_circuit_is_a_circuit-1 nil 3559650097
   ("" (auto-rewrite "finseq_appl")
    (("" (skeep)
      ((""
        (expand* "pre_Eulerian_circuit?" "circuit?"
         "pre_Eulerian_walk?" "pre_circuit?")
        (("" (flatten) (("" (assert) nil nil)) nil)) nil))
      nil))
    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)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (pre_Eulerian_circuit? const-decl "bool" Eulerian nil)
    (pre_Eulerian_walk? const-decl "bool" Eulerian nil)
    (pre_circuit? const-decl "bool" circuits nil)
    (circuit? const-decl "bool" circuits nil))
   shostak))
(Eulerian_circuit_is_circuit 0
  (Eulerian_circuit_is_circuit-1 nil 3561331484
   ("" (auto-rewrite "finseq_appl")
    (("" (skeep)
      ((""
        (expand* "Eulerian_circuit?" "pre_Eulerian_circuit?" "circuit?"
         "pre_circuit?" "pre_Eulerian_walk?")
        (("" (flatten) (("" (assert) nil nil)) nil)) nil))
      nil))
    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)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (Eulerian_circuit? const-decl "bool" Eulerian nil)
    (circuit? const-decl "bool" circuits nil)
    (pre_Eulerian_walk? const-decl "bool" Eulerian nil)
    (pre_circuit? const-decl "bool" circuits nil)
    (pre_Eulerian_circuit? const-decl "bool" Eulerian nil))
   shostak))
(Eulerian_walk_is_Eulerian_circuit 0
  (Eulerian_walk_is_Eulerian_circuit-1 nil 3561331889
   ("" (auto-rewrite "finseq_appl")
    (("" (skeep)
      ((""
        (expand* "Eulerian_circuit?" "pre_Eulerian_circuit?"
         "Eulerian_walk?" "pre_Eulerian_walk?")
        (("" (flatten) (("" (assert) nil nil)) nil)) nil))
      nil))
    nil)
   ((Eulerian_circuit? const-decl "bool" Eulerian nil)
    (Eulerian_walk? const-decl "bool" Eulerian nil)
    (pre_Eulerian_walk? const-decl "bool" Eulerian nil)
    (pre_Eulerian_circuit? const-decl "bool" Eulerian nil))
   shostak))
(circuit_subwalk_pre_Eulerian_TCC1 0
  (circuit_subwalk_pre_Eulerian_TCC1-1 nil 3563040767
   ("" (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)
    (edgetype type-eq-decl nil digraphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (predigraph type-eq-decl nil digraphs nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (digraph type-eq-decl nil digraphs 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (prewalk type-eq-decl nil walks nil)
    (T formal-type-decl nil Eulerian nil)
    (verts_in? const-decl "bool" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (edge? const-decl "bool" digraphs nil)
    (walk? const-decl "bool" walks nil)
    (pre_circuit? const-decl "bool" circuits nil)
    (circuit? const-decl "bool" circuits nil))
   nil))
(circuit_subwalk_pre_Eulerian 0
  (circuit_subwalk_pre_Eulerian-1 nil 3563040846
   ("" (skeep)
    (("" (lemma "circuit_subwalk_cycle")
      (("" (inst -1 "G" "w")
        (("" (assert)
          (("" (skeep)
            (("" (inst 1 "w1")
              (("" (assert)
                (("" (rewrite "cycle_is_pre_Eulerian_circuit") nil
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((T formal-type-decl nil Eulerian nil)
    (circuit_subwalk_cycle formula-decl nil cycles nil)
    (cycle_is_pre_Eulerian_circuit formula-decl nil Eulerian nil)
    (prewalk type-eq-decl nil walks 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)
    (finseq type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (digraph type-eq-decl nil digraphs nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (predigraph type-eq-decl nil digraphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (edgetype type-eq-decl nil digraphs nil))
   shostak))
(pre_Eulerian_circuit_prefix_TCC1 0
  (pre_Eulerian_circuit_prefix_TCC1-1 nil 3563121186
   ("" (subtype-tcc) nil nil)
   ((T formal-type-decl nil Eulerian nil)
    (verts_in? const-decl "bool" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (edge? const-decl "bool" digraphs nil)
    (walk? const-decl "bool" walks nil)
    (pre_circuit? const-decl "bool" circuits nil)
    (circuit? const-decl "bool" circuits nil)
    (no_repeat_subseq? const-decl "bool" Eulerian nil)
    (pre_Eulerian_walk? const-decl "bool" Eulerian nil)
    (pre_Eulerian_circuit? const-decl "bool" Eulerian nil)
    (O const-decl "finseq" finite_sequences nil))
   nil))
(pre_Eulerian_circuit_prefix 0
  (pre_Eulerian_circuit_prefix-1 nil 3563121188
   ("" (skeep)
    (("" (lemma "cycle_prefix")
      (("" (inst -1 "G" "w")
        (("" (assert)
          (("" (split)
            (("1" (rewrite "cycle_is_pre_Eulerian_circuit") nil nil)
             ("2" (skeep)
              (("2" (inst 2 "w1" "w2")
                (("2" (assert)
                  (("2" (hide-all-but (-2 2))
                    (("2" (rewrite "cycle_is_pre_Eulerian_circuit") nil
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((T formal-type-decl nil Eulerian nil)
    (cycle_prefix formula-decl nil cycles nil)
    (cycle_is_pre_Eulerian_circuit formula-decl nil Eulerian nil)
    (prewalk type-eq-decl nil walks 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)
    (finseq type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (digraph type-eq-decl nil digraphs nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (predigraph type-eq-decl nil digraphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (edgetype type-eq-decl nil digraphs nil))
   shostak))
(pre_Eulerian_circuit_o_circuit_TCC1 0
  (pre_Eulerian_circuit_o_circuit_TCC1-1 nil 3563123153
   ("" (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)
    (edgetype type-eq-decl nil digraphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (predigraph type-eq-decl nil digraphs nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (digraph type-eq-decl nil digraphs 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)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (prewalk type-eq-decl nil walks nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (T formal-type-decl nil Eulerian nil)
    (verts_in? const-decl "bool" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (edge? const-decl "bool" digraphs nil)
    (walk? const-decl "bool" walks nil)
    (pre_circuit? const-decl "bool" circuits nil)
    (circuit? const-decl "bool" circuits nil)
    (no_repeat_subseq? const-decl "bool" Eulerian nil)
    (pre_Eulerian_walk? const-decl "bool" Eulerian nil)
    (pre_Eulerian_circuit? const-decl "bool" Eulerian nil)
    (rest const-decl "finseq" seq_extras "structures/")
    (O const-decl "finseq" finite_sequences nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil))
   nil))
(pre_Eulerian_circuit_o_circuit 0
  (pre_Eulerian_circuit_o_circuit-1 nil 3563036557
   ("" (skeep)
    (("" (lemma "cycle_o_circuit")
      (("" (inst -1 "G" "w")
        (("" (assert)
          (("" (split)
            (("1" (hide -2 2)
              (("1" (rewrite "cycle_is_pre_Eulerian_circuit") nil nil))
              nil)
             ("2" (skeep)
              (("2" (inst 2 "w1" "w2")
                (("2" (assert)
                  (("2" (hide-all-but (-2 2))
                    (("2" (rewrite "cycle_is_pre_Eulerian_circuit") nil
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((T formal-type-decl nil Eulerian nil)
    (cycle_o_circuit formula-decl nil cycles nil)
    (cycle_is_pre_Eulerian_circuit formula-decl nil Eulerian nil)
    (prewalk type-eq-decl nil walks 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)
    (finseq type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (digraph type-eq-decl nil digraphs nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (predigraph type-eq-decl nil digraphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (edgetype type-eq-decl nil digraphs nil))
   shostak)))

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