(11steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc

At: dfs-cases 2
1. the_graph: Graph
2. the_obj: GraphObject(the_graph)
3. s: traversal(the_graph)
4. i: Vertices(the_graph)
5. x,y:Vertices(the_graph). the_obj.eq(x,y) x = y
6. T:Type, s:T, x:Vertices(the_graph), f:(TVertices(the_graph)T). L:Vertices(the_graph) List. (y:Vertices(the_graph). x-the_graph- > y (y L)) & the_obj.eacc(f,s,x) = list_accum(s',x'.f(s',x');s;L)
7. T:Type, s:T, f:(TVertices(the_graph)T). L:Vertices(the_graph) List. no_repeats(Vertices(the_graph);L) & (y:Vertices(the_graph). (y L)) & the_obj.vacc(f,s) = list_accum(s',x'.f(s',x');s;L)
8. ((inl(i) s) (inr(i) s))
s':traversal(the_graph). ((inr(i) s) (inl(i) s) s' = nil) & ((inr(i) s) & (inl(i) s) (s2:traversal(the_graph). s' = ([inl(i)] @ s2 @ [inr(i)]) traversal(the_graph))) & [inl(i) / (the_obj.eacc((s',j. dfs(the_obj;s';j)),[inr(i) / s],i))] = (s' @ s) traversal(the_graph)
By: Assert (L:Vertices(the_graph) List, s:traversal(the_graph). s2:traversal(the_graph). list_accum(s',j.dfs(the_obj;s';j);s;L) = (s2 @ s))
Generated subgoals:

1 L:Vertices(the_graph) List, s:traversal(the_graph). s2:traversal(the_graph). list_accum(s',j.dfs(the_obj;s';j);s;L) = (s2 @ s)4 steps
 
29. L:Vertices(the_graph) List, s:traversal(the_graph). s2:traversal(the_graph). list_accum(s',j.dfs(the_obj;s';j);s;L) = (s2 @ s)
s':traversal(the_graph). ((inr(i) s) (inl(i) s) s' = nil) & ((inr(i) s) & (inl(i) s) (s2:traversal(the_graph). s' = ([inl(i)] @ s2 @ [inr(i)]) traversal(the_graph))) & [inl(i) / (the_obj.eacc((s',j. dfs(the_obj;s';j)),[inr(i) / s],i))] = (s' @ s) traversal(the_graph)		4 steps

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(11steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc