Nuprl - Proof: connect-iff 1 1 1 2

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

At: connect-iff 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||

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

By: OrLeft THEN Unfold `last` -2 THEN Subst (||p|| ~ 1) -2

Generated subgoals:

1 10. p[(||p||-1)] = y
11. 1 < ||p||
||p|| ~ 1 1 step

2 10. p[(1-1)] = y
11. 1 < ||p||
x = y 1 step

About:

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

1	10. `p[(\|\|p\|\|-1)] = y` 11. `1 < \|\|p\|\|` `\|\|p\|\| ~ 1`	1 step

2	10. `p[(1-1)] = y` 11. `1 < \|\|p\|\|` `x = y`	1 step