At:
depthfirst induction2
For any graph
the_obj:GraphObject(the_graph), P:(Traversal
Prop). P(nil) 
(
s:Traversal, i:V. paren(V;s) 
no_repeats(V+V;s) 
P(s) 
P(dfs(the_obj;s;i))) 
paren(V;depthfirst(the_obj)) & no_repeats(V+V;depthfirst(the_obj)) & P(depthfirst(the_obj))
By:
RepeatFor 5 (Analyze 0)
THEN
Inst
Thm* For any graph
the_obj:GraphObject(the_graph).
L:V List. no_repeats(V;L) & (
y:V. (y
L)) & depthfirst(the_obj) = dfsl(the_obj;L)
[the_graph;the_obj]
THEN
ExRepD
THEN
HypSubst -1 0
THEN
Inst
Thm* dfsl-induction2
[the_graph;the_obj;
l,s. P(s)]
THEN
EasyHyp
Generated subgoals:
None
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