Nuprl - Some Definitions

	Some definitions of interest.

dfsl-traversal	Def dfsl-traversal(the_graph;L;s) == df-traversal(the_graph;s) & (i:Vertices(the_graph). (inl(i) s) L-the_graph- > i) & ((i:Vertices(the_graph). L-the_graph- > i non-trivial-loop(the_graph;i)) (L1,L2:Vertices(the_graph) List. L = (L1 @ L2) (s1,s2:traversal(the_graph). s = (s2 @ s1) traversal(the_graph) & paren(Vertices(the_graph);s1) & paren(Vertices(the_graph);s2) & (j:Vertices(the_graph). ((inl(j) s1) L1-the_graph- > j) & ((inl(j) s2) L2-the_graph- > j & L1-the_graph- > *j)))))

graphobj	Def GraphObject(the_graph) == eq:Vertices(the_graph)Vertices(the_graph)(x,y:Vertices(the_graph). (eq(x,y)) x = y)(eacc:(T:Type. (TVertices(the_graph)T)TVertices(the_graph)T)(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)) & eacc(f,s,x) = list_accum(s',x'.f(s',x');s;L))(vacc:(T:Type. (TVertices(the_graph)T)TT)(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)) & vacc(f,s) = list_accum(s',x'.f(s',x');s;L))Top))

	`Thm* the_graph:Graph. GraphObject(the_graph) Type{i'}`

gr_v	`Def Vertices(t) == 1of(t)`

	`Thm* t:Graph. Vertices(t) Type`

graph	`Def Graph == v:Typee:Type(evv)Top`

	`Thm* Graph Type{i'}`

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