Nuprl - Proof: dfl-traversal-consr 3

(11steps 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. j:Vertices(the_graph). (inr(j) s) (inl(j) s) j-the_graph- > *i
6. L-the_graph- > *i
7. i:Vertices(the_graph), s1,s2:traversal(the_graph). s = (s1 @ [inr(i)] @ s2) traversal(the_graph) (j:Vertices(the_graph). (inr(j) s2) (inl(j) s2) j-the_graph- > *i)
8. j:Vertices(the_graph). (inr(j) s) L-the_graph- > *j
9. i:Vertices(the_graph), s1,s2:traversal(the_graph). (j:Vertices(the_graph). i-the_graph- > *j non-trivial-loop(the_graph;j)) s = (s1 @ [inl(i)] @ s2) traversal(the_graph) L-the_graph- > *i
10. i@0: Vertices(the_graph)
11. s1: traversal(the_graph)
12. s2: traversal(the_graph)
13. j:Vertices(the_graph). i@0-the_graph- > *j non-trivial-loop(the_graph;j)
14. [inr(i) / s] = (s1 @ [inl(i@0)] @ s2) traversal(the_graph)

L-the_graph- > *i@0

By: Analyze -4 THEN All Reduce THEN SplitCons -1

Generated subgoals:

1 7. i:Vertices(the_graph), s1,s2:traversal(the_graph). s = (s1 @ [inr(i) / s2]) traversal(the_graph) (j:Vertices(the_graph). (inr(j) s2) (inl(j) s2) j-the_graph- > *i)
8. j:Vertices(the_graph). (inr(j) s) L-the_graph- > *j
9. i:Vertices(the_graph), s1,s2:traversal(the_graph). (j:Vertices(the_graph). i-the_graph- > *j non-trivial-loop(the_graph;j)) s = (s1 @ [inl(i) / s2]) traversal(the_graph) L-the_graph- > *i
10. i@0: Vertices(the_graph)
11. s2: traversal(the_graph)
12. j:Vertices(the_graph). i@0-the_graph- > *j non-trivial-loop(the_graph;j)
13. inr(i) = inl(i@0) Vertices(the_graph)+Vertices(the_graph)
14. s = s2
L-the_graph- > *i@0 1 step

2 7. i:Vertices(the_graph), s1,s2:traversal(the_graph). s = (s1 @ [inr(i) / s2]) traversal(the_graph) (j:Vertices(the_graph). (inr(j) s2) (inl(j) s2) j-the_graph- > *i)
8. j:Vertices(the_graph). (inr(j) s) L-the_graph- > *j
9. i:Vertices(the_graph), s1,s2:traversal(the_graph). (j:Vertices(the_graph). i-the_graph- > *j non-trivial-loop(the_graph;j)) s = (s1 @ [inl(i) / s2]) traversal(the_graph) L-the_graph- > *i
10. i@0: Vertices(the_graph)
11. u: Vertices(the_graph)+Vertices(the_graph)
12. v: (Vertices(the_graph)+Vertices(the_graph)) List
13. s2: traversal(the_graph)
14. j:Vertices(the_graph). i@0-the_graph- > *j non-trivial-loop(the_graph;j)
15. inr(i) = u
16. s = (v @ [inl(i@0) / s2]) traversal(the_graph)
L-the_graph- > *i@0 1 step

About:

(11steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc

1	7. `i:Vertices(the_graph), s1,s2:traversal(the_graph). s = (s1 @ [inr(i) / s2]) traversal(the_graph) (j:Vertices(the_graph). (inr(j) s2) (inl(j) s2) j-the_graph- > i)` 8. `j:Vertices(the_graph). (inr(j) s) L-the_graph- > j` 9. `i:Vertices(the_graph), s1,s2:traversal(the_graph). (j:Vertices(the_graph). i-the_graph- > j non-trivial-loop(the_graph;j)) s = (s1 @ [inl(i) / s2]) traversal(the_graph) L-the_graph- > i` 10. `i@0:` `Vertices(the_graph)` 11. `s2:` `traversal(the_graph)` 12. `j:Vertices(the_graph). i@0-the_graph- > j non-trivial-loop(the_graph;j)` 13. `inr(i) = inl(i@0) Vertices(the_graph)+Vertices(the_graph)` 14. `s = s2` `L-the_graph- > i@0`	1 step

2	7. `i:Vertices(the_graph), s1,s2:traversal(the_graph). s = (s1 @ [inr(i) / s2]) traversal(the_graph) (j:Vertices(the_graph). (inr(j) s2) (inl(j) s2) j-the_graph- > i)` 8. `j:Vertices(the_graph). (inr(j) s) L-the_graph- > j` 9. `i:Vertices(the_graph), s1,s2:traversal(the_graph). (j:Vertices(the_graph). i-the_graph- > j non-trivial-loop(the_graph;j)) s = (s1 @ [inl(i) / s2]) traversal(the_graph) L-the_graph- > i` 10. `i@0:` `Vertices(the_graph)` 11. `u:` `Vertices(the_graph)+Vertices(the_graph)` 12. `v:` `(Vertices(the_graph)+Vertices(the_graph)) List` 13. `s2:` `traversal(the_graph)` 14. `j:Vertices(the_graph). i@0-the_graph- > j non-trivial-loop(the_graph;j)` 15. `inr(i) = u` 16. `s = (v @ [inl(i@0) / s2]) traversal(the_graph)` `L-the_graph- > i@0`	1 step