Nuprl - Proof: dfl-traversal-consl 3

(10steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc

1. the_graph: Graph
2. L: Vertices(the_graph) List
3. i: Vertices(the_graph)
4. s: traversal(the_graph)
5. (inr(i) s)
6. dfl-traversal(the_graph;L;s)
7. i@0: Vertices(the_graph)
8. s1: traversal(the_graph)
9. s2: traversal(the_graph)
10. j:Vertices(the_graph). i@0-the_graph- > *j non-trivial-loop(the_graph;j)
11. [inl(i) / s] = (s1 @ [inl(i@0)] @ s2) traversal(the_graph)

L-the_graph- > *i@0

By: Analyze -4 THEN All Reduce THEN SplitCons -1 THEN Try ((Reduce 0) THEN (Reduce 0) THEN (Unfold `label` 0))

Generated subgoals:

1 8. s2: traversal(the_graph)
9. j:Vertices(the_graph). i@0-the_graph- > *j non-trivial-loop(the_graph;j)
10. inl(i) = inl(i@0) Vertices(the_graph)+Vertices(the_graph)
11. s = s2
L-the_graph- > *i@0 1 step

2 8. u: Vertices(the_graph)+Vertices(the_graph)
9. v: (Vertices(the_graph)+Vertices(the_graph)) List
10. s2: traversal(the_graph)
11. j:Vertices(the_graph). i@0-the_graph- > *j non-trivial-loop(the_graph;j)
12. inl(i) = u
13. s = (v @ [inl(i@0) / s2]) traversal(the_graph)
L-the_graph- > *i@0 1 step

About:

(10steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc

1	8. `s2:` `traversal(the_graph)` 9. `j:Vertices(the_graph). i@0-the_graph- > j non-trivial-loop(the_graph;j)` 10. `inl(i) = inl(i@0) Vertices(the_graph)+Vertices(the_graph)` 11. `s = s2` `L-the_graph- > i@0`	1 step

2	8. `u:` `Vertices(the_graph)+Vertices(the_graph)` 9. `v:` `(Vertices(the_graph)+Vertices(the_graph)) List` 10. `s2:` `traversal(the_graph)` 11. `j:Vertices(the_graph). i@0-the_graph- > j non-trivial-loop(the_graph;j)` 12. `inl(i) = u` 13. `s = (v @ [inl(i@0) / s2]) traversal(the_graph)` `L-the_graph- > i@0`	1 step