Nuprl - Proof: connect-iff 1 1 1 1 2

(28steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc

At: connect-iff 1 1 1 1 2

1. the_graph: Graph
2. x,y:Vertices(the_graph). Dec(x = y)
3. x: Vertices(the_graph)
4. y: Vertices(the_graph)
5. n:
6. p: Vertices(the_graph) List
7. p1:Vertices(the_graph) List. ||p1|| < ||p|| path(the_graph;p1) p1[0] = x last(p1) = y x = y (z:Vertices(the_graph). z = x & x-the_graph- > z & z-the_graph- > *y)
8. path(the_graph;p)
9. p[0] = x
10. last(p) = y
11. 1 < ||p||
12. p[1] = x p[1] = x

x = y (z:Vertices(the_graph). z = x & x-the_graph- > z & z-the_graph- > *y)

By: AssertBY path(the_graph;tl(p)) (BackThru Thm* For any graph p:V List. 1 < ||p|| path(the_graph;p) path(the_graph;tl(p)))

Generated subgoal:

1 13. path(the_graph;tl(p))
x = y (z:Vertices(the_graph). z = x & x-the_graph- > z & z-the_graph- > *y) 11 steps

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(28steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc