Nuprl - Proof: dfl-traversal-consr 1 1

(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. s2: traversal(the_graph)
12. [inr(i) / s] = [inr(i@0) / s2]
13. j: Vertices(the_graph)
14. (inr(j) s2)
15. (inl(j) s2)

j-the_graph- > *i@0

By: SplitCons -4 THEN Subst (i@0 = i) 0 THEN Try (BackThruSomeHyp THEN (HypSubst -1 0))

Generated subgoal:

1 12. j: Vertices(the_graph)
13. (inr(j) s2)
14. (inl(j) s2)
15. inr(i) = inr(i@0) Vertices(the_graph)+Vertices(the_graph)
16. s = s2
i@0 = i 1 step

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