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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: invfun.ml   Sprache: Lisp

Original von: PVS©

(meng_scaff_defs
 (H_TCC1 0
  (H_TCC1-1 nil 3507100603
   ("" (skosimp*)
    (("" (expand "subgraph?")
      (("" (split 1)
        (("1" (expand "subset?")
          (("1" (skosimp*)
            (("1" (expand "path_comp")
              (("1" (expand "subgraph")
                (("1" (expand "del_vert")
                  (("1" (expand "member")
                    (("1" (flatten)
                      (("1" (hide -2)
                        (("1" (expand "remove")
                          (("1" (expand "member")
                            (("1" (flatten)
                              (("1" (propax) nil)))))))))))))))))))))))
         ("2" (expand "subset?")
          (("2" (skosimp*)
            (("2" (expand "member")
              (("2" (expand "path_comp")
                (("2" (expand "subgraph")
                  (("2" (flatten)
                    (("2" (hide -2)
                      (("2" (expand "del_vert")
                        (("2" (flatten)
                          (("2" (propax) nil))))))))))))))))))))))))
    nil)
   ((subgraph? const-decl "bool" subgraphs nil)
    (subset? const-decl "bool" sets nil)
    (path_comp const-decl "Subgraph(G)" meng_scaff_defs nil)
    (del_vert const-decl "graph[T]" graph_ops nil)
    (remove const-decl "set" sets nil)
    (member const-decl "bool" sets nil)
    (subgraph const-decl "Subgraph(G)" subgraphs nil))
   nil))
 (incident_TCC1 0
  (incident_TCC1-1 nil 3507100603
   ("" (skosimp*)
    (("" (lemma "finite_subset[Dbl]")
      (("" (inst?)
        (("" (inst -1 "edges(G!1)")
          (("" (assert)
            (("" (hide 2)
              (("" (expand "subset?")
                (("" (skosimp*)
                  (("" (expand "member")
                    (("" (skosimp*) nil))))))))))))))))))
    nil)
   ((Dbl type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-type-decl nil meng_scaff_defs nil)
    (finite_subset formula-decl nil finite_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (member const-decl "bool" sets nil)
    (subset? const-decl "bool" sets nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (H const-decl "Subgraph(G)" meng_scaff_defs nil)
    (Subgraph type-eq-decl nil subgraphs nil)
    (subgraph? const-decl "bool" subgraphs nil)
    (graph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pregraph type-eq-decl nil graphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (doubleton type-eq-decl nil doubletons nil))
   nil))
 (meng_TCC1 0
  (meng_TCC1-1 nil 3507100603
   ("" (skosimp*) (("" (inst?) (("" (assertnil)))) nil)
   ((T formal-type-decl nil meng_scaff_defs nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (set type-eq-decl nil sets nil)
    (/= const-decl "boolean" notequal nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (graph type-eq-decl nil graphs nil))
   nil))
 (meng_TCC2 0
  (meng_TCC2-1 nil 3507100603
   ("" (skosimp*) (("" (inst?) (("" (assertnil)))) nil)
   ((T formal-type-decl nil meng_scaff_defs nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (set type-eq-decl nil sets nil)
    (/= const-decl "boolean" notequal nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (graph type-eq-decl nil graphs nil))
   nil))
 (meng_TCC3 0
  (meng_TCC3-1 nil 3507100603
   ("" (skosimp*)
    (("" (expand "add")
      (("" (flatten)
        (("" (expand "member")
          (("" (flatten)
            (("" (split -1)
              (("1" (replace -1 * rl)
                (("1" (hide -1)
                  (("1" (expand "dbl") (("1" (ground) nil)))))))
               ("2" (replace -1 * rl)
                (("2" (hide -1)
                  (("2" (expand "dbl") (("2" (ground) nil)))))))
               ("3" (expand "union")
                (("3" (expand "member")
                  (("3" (split -1)
                    (("1" (typepred "H(G!1, x!1, w1!1, w2!1)")
                      (("1" (inst?)
                        (("1" (assert)
                          (("1" (inst?) (("1" (assertnil)))))))))
                     ("2" (expand "incident")
                      (("2" (skosimp*)
                        (("2" (replace -2)
                          (("2" (hide -2)
                            (("2" (expand "dbl")
                              (("2"
                                (split -)
                                (("1"
                                  (replace -1)
                                  (("1" (propax) nil)))
                                 ("2"
                                  (replace -1)
                                  (("2" (propax) nil)))))))))))))))
                     ("3" (expand "incident")
                      (("3" (skosimp*)
                        (("3" (replace -2)
                          (("3" (hide -2)
                            (("3" (expand "dbl" -3)
                              (("3"
                                (split -3)
                                (("1"
                                  (replace -1)
                                  (("1" (propax) nil)))
                                 ("2"
                                  (assert)
                                  nil))))))))))))))))))))))))))))))
    nil)
   ((add const-decl "(nonempty?)" sets nil)
    (member const-decl "bool" sets nil)
    (dbl const-decl "set[T]" doubletons nil)
    (nil application-judgement "finite_set[T]" meng_scaff_defs nil)
    (incident const-decl "finite_set[doubleton[T]]" meng_scaff_defs
     nil)
    (H const-decl "Subgraph(G)" meng_scaff_defs nil)
    (Subgraph type-eq-decl nil subgraphs nil)
    (subgraph? const-decl "bool" subgraphs nil)
    (graph type-eq-decl nil graphs nil)
    (pregraph type-eq-decl nil graphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (doubleton type-eq-decl nil doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil meng_scaff_defs nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (union const-decl "set" sets nil))
   nil))
 (vert_H_s 0
  (vert_H_s-1 nil 3507100603
   ("" (skosimp*)
    (("" (assert)
      (("" (expand "H")
        (("" (expand "path_comp")
          (("" (expand "subgraph")
            (("" (expand "del_vert")
              (("" (expand "remove")
                (("" (expand "member")
                  (("" (expand "path_verts")
                    (("" (expand "walk_from?")
                      (("" (inst + "gen_seq1(G!1,s!1)")
                        (("" (expand "gen_seq1")
                          (("" (expand "walk?")
                            (("" (expand "verts_in?")
                              ((""
                                (propax)
                                nil))))))))))))))))))))))))))))
    nil)
   ((path_comp const-decl "Subgraph(G)" meng_scaff_defs nil)
    (del_vert const-decl "graph[T]" graph_ops nil)
    (member const-decl "bool" sets nil)
    (walk_from? const-decl "bool" walks nil)
    (walk? const-decl "bool" walks nil)
    (gen_seq1 const-decl "Seq(G)" walks nil)
    (Seq type-eq-decl nil walks nil)
    (verts_in? const-decl "bool" walks nil)
    (graph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pregraph type-eq-decl nil graphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (set type-eq-decl nil sets nil)
    (prewalk type-eq-decl nil walks 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)
    (finseq type-eq-decl nil finite_sequences nil)
    (T formal-type-decl nil meng_scaff_defs nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (path_verts const-decl "set[T]" paths nil)
    (remove const-decl "set" sets nil)
    (subgraph const-decl "Subgraph(G)" subgraphs nil)
    (H const-decl "Subgraph(G)" meng_scaff_defs nil))
   nil))
 (path_H_W 0
  (path_H_W-1 nil 3507100603
   ("" (skosimp*)
    (("" (expand "path?")
      (("" (flatten)
        (("" (hide -2)
          (("" (expand "walk?")
            (("" (flatten)
              (("" (hide -2)
                (("" (expand "verts_in?")
                  (("" (expand "H")
                    (("" (expand "path_comp")
                      (("" (expand "subgraph")
                        (("" (expand "del_vert")
                          (("" (expand "remove")
                            (("" (expand "member")
                              ((""
                                (expand "verts_of")
                                ((""
                                  (expand "finseq_appl")
                                  ((""
                                    (split 1)
                                    (("1"
                                      (skosimp*)
                                      (("1"
                                        (inst?)
                                        (("1" (assertnil)))))
                                     ("2"
                                      (assert)
                                      (("2"
                                        (skosimp*)
                                        (("2"
                                          (inst?)
                                          (("2"
                                            (assert)
                                            nil))))))))))))))))))))))))))))))))))))))))
    nil)
   ((path? const-decl "bool" paths nil)
    (verts_in? const-decl "bool" walks nil)
    (path_comp const-decl "Subgraph(G)" meng_scaff_defs nil)
    (del_vert const-decl "graph[T]" graph_ops nil)
    (member const-decl "bool" sets nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (below type-eq-decl nil naturalnumbers nil)
    (prewalk type-eq-decl nil walks nil)
    (> const-decl "bool" reals nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (T formal-type-decl nil meng_scaff_defs nil)
    (below type-eq-decl nil nat_types 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_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)
    (verts_of const-decl "finite_set[T]" walks nil)
    (remove const-decl "set" sets nil)
    (subgraph const-decl "Subgraph(G)" subgraphs nil)
    (H const-decl "Subgraph(G)" meng_scaff_defs nil)
    (walk? const-decl "bool" walks nil))
   nil))
 (path_comp_in 0
  (path_comp_in-1 nil 3507100603
   ("" (skosimp*)
    (("" (expand "path?")
      (("" (split 1)
        (("1" (flatten)
          (("1" (typepred "H(G!1, s!1, w1!1, w2!1)")
            (("1" (hide -1 -4)
              (("1" (lemma "walk?_subgraph")
                (("1" (inst?)
                  (("1" (inst?) (("1" (assertnil nil)) nil)) nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (flatten) nil nil))
        nil))
      nil))
    nil)
   ((path? const-decl "bool" paths 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)
    (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)
    (prewalk type-eq-decl nil walks nil)
    (walk?_subgraph formula-decl nil subgraph_paths nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (T formal-type-decl nil meng_scaff_defs nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (graph type-eq-decl nil graphs nil)
    (subgraph? const-decl "bool" subgraphs nil)
    (Subgraph type-eq-decl nil subgraphs nil)
    (H const-decl "Subgraph(G)" meng_scaff_defs nil))
   nil))
 (walk?_H_TCC1 0
  (walk?_H_TCC1-1 nil 3507100603 ("" (subtype-tcc) nil nil)
   ((T formal-type-decl nil meng_scaff_defs nil)
    (verts_in? const-decl "bool" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (/= const-decl "boolean" notequal nil)
    (edge? const-decl "bool" graphs nil)
    (walk? const-decl "bool" walks nil)
    (nil application-judgement "finite_set[T]" meng_scaff_defs nil))
   nil))
 (walk?_H 0
  (walk?_H-1 nil 3507100603
   ("" (skosimp*)
    (("" (expand "H")
      (("" (expand "path_comp")
        (("" (expand "walk?")
          (("" (flatten)
            (("" (split +)
              (("1" (hide -2)
                (("1" (expand "verts_in?")
                  (("1" (skosimp*)
                    (("1" (inst?)
                      (("1" (expand "subgraph")
                        (("1" (expand "del_vert")
                          (("1" (expand "remove")
                            (("1" (expand "member")
                              (("1"
                                (assert)
                                (("1"
                                  (expand "verts_of")
                                  (("1"
                                    (inst?)
                                    (("1"
                                      (expand "finseq_appl")
                                      (("1"
                                        (inst?)
                                        (("1"
                                          (assert)
                                          (("1"
                                            (expand "path_verts")
                                            (("1"
                                              (expand "walk_from?")
                                              (("1"
                                                (inst 1 "p!1^(0,i!1)")
                                                (("1"
                                                  (expand*
                                                   "^"
                                                   min
                                                   empty_seq)
                                                  (("1"
                                                    (expand "walk?")
                                                    (("1"
                                                      (split +)
                                                      (("1"
                                                        (expand
                                                         "verts_in?")
                                                        (("1"
                                                          (skosimp*)
                                                          (("1"
                                                            (reveal -1)
                                                            (("1"
                                                              (inst?)
                                                              (("1"
                                                                (assert)
                                                                (("1"
                                                                  (reveal
                                                                   2
                                                                   3)
                                                                  (("1"
                                                                    (expand
                                                                     "finseq_appl")
                                                                    (("1"
                                                                      (hide
                                                                       4
                                                                       5
                                                                       -2)
                                                                      (("1"
                                                                        (inst?)
                                                                        (("1"
                                                                          (inst?)
                                                                          (("1"
                                                                            (assert)
                                                                            nil)))))))))))))))))))))
                                                       ("2"
                                                        (expand
                                                         "finseq_appl")
                                                        (("2"
                                                          (skosimp*)
                                                          (("2"
                                                            (expand
                                                             "edge?")
                                                            (("2"
                                                              (hide
                                                               -2
                                                               2
                                                               3)
                                                              (("2"
                                                                (reveal
                                                                 -3)
                                                                (("2"
                                                                  (inst
                                                                   -
                                                                   "n!1")
                                                                  (("2"
                                                                    (assert)
                                                                    (("2"
                                                                      (expand
                                                                       "finseq_appl")
                                                                      (("2"
                                                                        (expand
                                                                         "edge?")
                                                                        (("2"
                                                                          (flatten)
                                                                          (("2"
                                                                            (assert)
                                                                            (("2"
                                                                              (hide
                                                                               -1
                                                                               -3)
                                                                              (("2"
                                                                                (reveal
                                                                                 4
                                                                                 5)
                                                                                (("2"
                                                                                  (expand
                                                                                   "finseq_appl")
                                                                                  (("2"
                                                                                    (inst-cp
                                                                                     +
                                                                                     "n!1")
                                                                                    (("2"
                                                                                      (inst
                                                                                       +
                                                                                       "n!1+1")
                                                                                      (("2"
                                                                                        (inst-cp
                                                                                         +
                                                                                         "n!1")
                                                                                        (("2"
                                                                                          (inst
                                                                                           +
                                                                                           "n!1+1")
                                                                                          (("2"
                                                                                            (expand
                                                                                             "dbl")
                                                                                            (("2"
                                                                                              (ground)
                                                                                              nil)))))))))))))))))))))))))))))))))))))))))))))
                                                 ("2"
                                                  (expand*
                                                   "^"
                                                   min
                                                   empty_seq)
                                                  (("2"
                                                    (assert)
                                                    nil)))))))))))))))))))))))))))))))))))))
               ("2" (skosimp*)
                (("2" (expand "finseq_appl")
                  (("2" (expand "edge?")
                    (("2" (inst?)
                      (("2" (assert)
                        (("2" (flatten)
                          (("2" (assert)
                            (("2" (expand "subgraph")
                              (("2"
                                (expand "del_vert")
                                (("2"
                                  (split +)
                                  (("1"
                                    (expand "verts_of" 2)
                                    (("1"
                                      (inst-cp + "n!1")
                                      (("1"
                                        (inst + "n!1+1")
                                        (("1"
                                          (expand "finseq_appl")
                                          (("1"
                                            (expand "dbl")
                                            (("1"
                                              (ground)
                                              nil)))))))))))
                                   ("2"
                                    (expand "verts_of" 3)
                                    (("2"
                                      (inst-cp + "n!1")
                                      (("2"
                                        (inst + "n!1+1")
                                        (("2"
                                          (expand "finseq_appl")
                                          (("2"
                                            (expand "dbl")
                                            (("2"
                                              (ground)
                                              nil)))))))))))
                                   ("3"
                                    (skosimp*)
                                    (("3"
                                      (expand "path_verts")
                                      (("3"
                                        (expand "walk_from?")
                                        (("3"
                                          (expand "dbl")
                                          (("3"
                                            (split -1)
                                            (("1"
                                              (inst 1 "p!1^(0,n!1)")
                                              (("1"
                                                (expand*
                                                 "^"
                                                 min
                                                 empty_seq)
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (expand "walk?")
                                                    (("1"
                                                      (split +)
                                                      (("1"
                                                        (expand
                                                         "verts_in?")
                                                        (("1"
                                                          (skosimp*)
                                                          (("1"
                                                            (expand
                                                             "remove")
                                                            (("1"
                                                              (expand
                                                               "member")
                                                              (("1"
                                                                (inst?)
                                                                (("1"
                                                                  (assert)
                                                                  (("1"
                                                                    (expand
                                                                     "verts_of")
                                                                    (("1"
                                                                      (inst
                                                                       +
                                                                       "i!1")
                                                                      (("1"
                                                                        (inst
                                                                         +
                                                                         "i!1")
                                                                        (("1"
                                                                          (expand
                                                                           "finseq_appl")
                                                                          (("1"
                                                                            (ground)
                                                                            nil)))))))))))))))))))))
                                                       ("2"
                                                        (skosimp*)
                                                        (("2"
                                                          (expand
                                                           "finseq_appl")
                                                          (("2"
                                                            (expand
                                                             "edge?")
                                                            (("2"
                                                              (assert)
                                                              (("2"
                                                                (reveal
                                                                 -1)
                                                                (("2"
                                                                  (inst?)
                                                                  (("2"
                                                                    (assert)
                                                                    (("2"
                                                                      (flatten)
                                                                      (("2"
                                                                        (assert)
                                                                        (("2"
                                                                          (expand
                                                                           "dbl")
                                                                          (("2"
                                                                            (expand
                                                                             "verts_of")
                                                                            (("2"
                                                                              (inst-cp
                                                                               +
                                                                               "n!2")
                                                                              (("2"
                                                                                (inst
                                                                                 +
                                                                                 "n!2+1")
                                                                                (("2"
                                                                                  (inst-cp
                                                                                   +
                                                                                   "n!2")
                                                                                  (("2"
                                                                                    (inst
                                                                                     +
                                                                                     "n!2+1")
                                                                                    (("2"
                                                                                      (expand
                                                                                       "finseq_appl")
                                                                                      (("2"
                                                                                        (ground)
                                                                                        nil)))))))))))))))))))))))))))))))))))))))))
                                               ("2"
                                                (expand*
                                                 "^"
                                                 min
                                                 empty_seq)
                                                (("2" (assertnil)))))
                                             ("2"
                                              (inst 1 "p!1^(0,n!1+1)")
                                              (("1"
                                                (expand*
                                                 "^"
                                                 min
                                                 empty_seq)
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (expand "walk?")
                                                    (("1"
                                                      (split +)
                                                      (("1"
                                                        (expand
                                                         "verts_in?")
                                                        (("1"
                                                          (skosimp*)
                                                          (("1"
                                                            (expand
                                                             "remove")
                                                            (("1"
                                                              (expand
                                                               "member")
                                                              (("1"
                                                                (inst?)
                                                                (("1"
                                                                  (assert)
                                                                  (("1"
                                                                    (expand
                                                                     "verts_of")
                                                                    (("1"
                                                                      (inst-cp
                                                                       +
                                                                       "i!1")
                                                                      (("1"
                                                                        (inst
                                                                         +
                                                                         "i!1+1")
                                                                        (("1"
                                                                          (inst-cp
                                                                           +
                                                                           "i!1")
                                                                          (("1"
                                                                            (inst
                                                                             +
                                                                             "i!1+1")
                                                                            (("1"
                                                                              (expand
                                                                               "finseq_appl")
                                                                              (("1"
                                                                                (assert)
                                                                                nil)))
                                                                             ("2"
                                                                              (assert)
                                                                              (("2"
                                                                                (typepred
                                                                                 "i!1")
                                                                                (("2"
                                                                                  (expand
                                                                                   "finseq_appl")
                                                                                  (("2"
                                                                                    (assert)
                                                                                    nil)))))))))))
                                                                         ("2"
                                                                          (expand
                                                                           "finseq_appl")
                                                                          (("2"
                                                                            (assert)
                                                                            (("2"
                                                                              (typepred
                                                                               "i!1")
                                                                              (("2"
                                                                                (inst?)
                                                                                (("2"
                                                                                  (assert)
                                                                                  nil)))))))))))))))))))))))))))
                                                       ("2"
                                                        (skosimp*)
                                                        (("2"
                                                          (expand
                                                           "edge?")
                                                          (("2"
                                                            (expand
                                                             "finseq_appl")
                                                            (("2"
                                                              (reveal
                                                               -1)
                                                              (("2"
                                                                (inst?)
                                                                (("2"
                                                                  (assert)
                                                                  (("2"
                                                                    (flatten)
                                                                    (("2"
                                                                      (assert)
                                                                      (("2"
                                                                        (expand
                                                                         "verts_of")
                                                                        (("2"
                                                                          (expand
                                                                           "finseq_appl")
                                                                          (("2"
                                                                            (inst-cp
                                                                             +
                                                                             "n!2")
                                                                            (("2"
                                                                              (inst
                                                                               +
                                                                               "n!2+1")
                                                                              (("2"
                                                                                (inst-cp
                                                                                 +
                                                                                 "n!2")
                                                                                (("2"
                                                                                  (inst
                                                                                   +
                                                                                   "n!2+1")
                                                                                  (("2"
                                                                                    (expand
                                                                                     "dbl")
                                                                                    (("2"
                                                                                      (ground)
                                                                                      nil)))))))))))))))))))))))))))))))))))))))
                                               ("2"
                                                (expand*
                                                 "^"
                                                 min
                                                 empty_seq)
                                                (("2"
                                                  (assert)
                                                  nil))))))))))))))))))))))))))))))))))))))))))))))
    nil)
   ((H const-decl "Subgraph(G)" meng_scaff_defs nil)
    (walk? const-decl "bool" walks nil)
    (verts_in? const-decl "bool" walks 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)
    (below type-eq-decl nil nat_types nil)
    (T formal-type-decl nil meng_scaff_defs 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)
    (del_vert const-decl "graph[T]" graph_ops nil)
    (member const-decl "bool" sets nil)
    (verts_of const-decl "finite_set[T]" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (walk_from? const-decl "bool" walks nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (nat_min application-judgement "{k: nat | k <= i AND k <= j}"
     real_defs nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (dbl const-decl "set[T]" doubletons nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (edge? const-decl "bool" graphs nil)
    (nil application-judgement "finite_set[T]" meng_scaff_defs nil)
    (i!1 skolem-const-decl "below(length(p!1))" meng_scaff_defs nil)
    (p!1 skolem-const-decl "prewalk[T]" meng_scaff_defs nil)
    (^ const-decl "finseq" finite_sequences nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (path_verts const-decl "set[T]" paths nil)
    (remove const-decl "set" sets nil)
    (subgraph const-decl "Subgraph(G)" subgraphs nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (i!1 skolem-const-decl "below(2 + n!1)" meng_scaff_defs nil)
    (n!1 skolem-const-decl "nat" meng_scaff_defs nil)
    (path_comp const-decl "Subgraph(G)" meng_scaff_defs nil))
   nil))
 (vert_meng_sub_TCC1 0
  (vert_meng_sub_TCC1-1 nil 3507100603 ("" (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)
    (T formal-type-decl nil meng_scaff_defs nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (graph type-eq-decl nil graphs nil)
    (/= const-decl "boolean" notequal nil)
    (disjoint? const-decl "bool" meng_scaff_defs nil)
    (in? const-decl "bool" meng_scaff_defs nil))
   nil))
 (vert_meng_sub_TCC2 0
  (vert_meng_sub_TCC2-1 nil 3507100603 ("" (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)
    (T formal-type-decl nil meng_scaff_defs nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (graph type-eq-decl nil graphs nil)
    (/= const-decl "boolean" notequal nil)
    (disjoint? const-decl "bool" meng_scaff_defs nil)
    (in? const-decl "bool" meng_scaff_defs nil))
   nil))
 (vert_meng_sub_TCC3 0
  (vert_meng_sub_TCC3-1 nil 3507100603 ("" (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)
    (T formal-type-decl nil meng_scaff_defs nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (graph type-eq-decl nil graphs nil)
    (/= const-decl "boolean" notequal nil)
    (disjoint? const-decl "bool" meng_scaff_defs nil)
    (in? const-decl "bool" meng_scaff_defs nil))
   nil))
 (vert_meng_sub_TCC4 0
  (vert_meng_sub_TCC4-1 nil 3507100603 ("" (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)
    (T formal-type-decl nil meng_scaff_defs nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (graph type-eq-decl nil graphs nil)
    (/= const-decl "boolean" notequal nil)
    (disjoint? const-decl "bool" meng_scaff_defs nil)
    (in? const-decl "bool" meng_scaff_defs nil))
   nil))
 (vert_meng_sub 0
  (vert_meng_sub-1 nil 3507100603
   ("" (skosimp*)
    (("" (expand "subset?")
      (("" (expand "member")
        (("" (skosimp*)
          (("" (expand "meng")
            (("" (expand "add")
              (("" (expand "member")
                (("" (assert)
                  (("" (expand "H")
                    (("" (expand "path_comp")
                      (("" (expand "subgraph")
                        (("" (expand "del_vert")
                          (("" (expand "remove")
                            (("" (expand "member")
                              ((""
                                (expand "in?")
                                ((""
                                  (flatten)
                                  ((""
                                    (expand "disjoint?")
                                    ((""
                                      (flatten)
                                      ((""
                                        (assert)
                                        nil))))))))))))))))))))))))))))))))))))
    nil)
   ((subset? const-decl "bool" sets nil)
    (add const-decl "(nonempty?)" sets nil)
    (path_comp const-decl "Subgraph(G)" meng_scaff_defs nil)
    (del_vert const-decl "graph[T]" graph_ops nil)
    (disjoint? const-decl "bool" meng_scaff_defs nil)
    (in? const-decl "bool" meng_scaff_defs nil)
    (remove const-decl "set" sets nil)
    (subgraph const-decl "Subgraph(G)" subgraphs nil)
    (H const-decl "Subgraph(G)" meng_scaff_defs nil)
    (meng const-decl "graph[T]" meng_scaff_defs nil)
    (member const-decl "bool" sets nil))
   nil))
 (del_vert_comm 0
  (del_vert_comm-1 nil 3507100603
   ("" (skosimp*)
    (("" (apply-extensionality 1 :hide? t)
      (("1" (apply-extensionality 1 :hide? t)
        (("1" (expand "del_vert")
          (("1" (iff 1) (("1" (ground) nil)))))))
       ("2" (apply-extensionality 1 :hide? t)
        (("2" (expand "del_vert")
          (("2" (expand "remove")
            (("2" (expand "member")
              (("2" (iff 1) (("2" (ground) nil))))))))))))))
    nil)
   ((T formal-type-decl nil meng_scaff_defs nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (del_vert const-decl "graph[T]" graph_ops nil)
    (graph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (member const-decl "bool" sets nil)
    (remove const-decl "set" sets nil))
   nil))
 (H_comm 0
  (H_comm-1 nil 3507100603
   ("" (skosimp*)
    (("" (expand "H")
      (("" (expand "path_comp")
        (("" (rewrite "del_vert_comm"nil))))))
    nil)
   ((H const-decl "Subgraph(G)" meng_scaff_defs nil)
    (del_vert_comm formula-decl nil meng_scaff_defs nil)
    (T formal-type-decl nil meng_scaff_defs nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (graph type-eq-decl nil graphs nil)
    (path_comp const-decl "Subgraph(G)" meng_scaff_defs nil))
   nil))
 (incident_comm 0
  (incident_comm-1 nil 3507100603
   ("" (skosimp*)
    (("" (expand "incident") (("" (rewrite "H_comm"nil)))) nil)
   ((incident const-decl "finite_set[doubleton[T]]" meng_scaff_defs
     nil)
    (graph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pregraph type-eq-decl nil graphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-type-decl nil meng_scaff_defs nil)
    (H_comm formula-decl nil meng_scaff_defs nil))
   nil))
 (meng_comm_TCC1 0
  (meng_comm_TCC1-1 nil 3507100603 ("" (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)
    (T formal-type-decl nil meng_scaff_defs nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (graph type-eq-decl nil graphs nil)
    (/= const-decl "boolean" notequal nil))
   nil))
 (meng_comm_TCC2 0
  (meng_comm_TCC2-1 nil 3507100603 ("" (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)
    (T formal-type-decl nil meng_scaff_defs nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (graph type-eq-decl nil graphs nil)
    (/= const-decl "boolean" notequal nil))
   nil))
 (meng_comm 0
  (meng_comm-1 nil 3507100603
   ("" (skosimp*)
    (("" (hide -1)
      (("" (expand "meng")
        ((""
          (case-replace
           "H(G!1, t!1, w2!1, w1!1) = H(G!1, t!1, w1!1, w2!1)")
          (("1" (split 3)
            (("1" (hide -1)
              (("1" (apply-extensionality 1 :hide? t)
                (("1" (expand "add")
                  (("1" (expand "member")
                    (("1" (iff) (("1" (ground) nil)))))))))))
             ("2" (apply-extensionality 1 :hide? t)
              (("1" (expand "union")
                (("1" (expand "add")
                  (("1" (expand "member")
                    (("1" (iff)
                      (("1" (lemma "incident_comm")
                        (("1" (inst?)
                          (("1" (lemma "incident_comm")
                            (("1"
                              (inst -1 "G!1" "t!1" "w2!1" "w1!1"
                               "w2!1")
                              (("1"
                                (replace -1)
                                (("1"
                                  (hide -1)
                                  (("1"
                                    (replace -1)
                                    (("1"
                                      (hide -1)
                                      (("1"
                                        (ground)
                                        nil)))))))))))))))))))))))))
               ("2" (inst?) (("2" (assertnil)))
               ("3" (inst?) (("3" (assertnil)))))))
           ("2" (hide 4)
            (("2" (lemma "H_comm") (("2" (inst?) nil))))))))))))
    nil)
   ((T formal-type-decl nil meng_scaff_defs nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (graph type-eq-decl nil graphs nil)
    (subgraph? const-decl "bool" subgraphs nil)
    (Subgraph type-eq-decl nil subgraphs nil)
    (H const-decl "Subgraph(G)" meng_scaff_defs nil)
    (incident const-decl "finite_set[doubleton[T]]" meng_scaff_defs
     nil)
    (is_finite const-decl "bool" finite_sets nil)
    (union const-decl "set" sets nil)
    (nil application-judgement "finite_set[T]" meng_scaff_defs nil)
    (finite_union application-judgement "finite_set" finite_sets nil)
    (incident_comm formula-decl nil meng_scaff_defs nil)
    (member const-decl "bool" sets nil)
    (nonempty_add_finite application-judgement "non_empty_finite_set"
     finite_sets nil)
    (nonempty? const-decl "bool" sets nil)
    (add const-decl "(nonempty?)" sets nil)
    (H_comm formula-decl nil meng_scaff_defs nil)
    (meng const-decl "graph[T]" meng_scaff_defs nil))
   nil)))


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