(3steps total)
PrintForm
Definitions
Lemmas
graph
1
3
Sections
Graphs
Doc
At:
dfsl-induction1
1
1.
the_graph:
Graph
2.
the_obj:
GraphObject(the_graph)
3.
P:
(Vertices(the_graph) List)
traversal(the_graph)
Prop
4.
P(nil,nil)
5.
L:Vertices(the_graph) List, s:traversal(the_graph), i:Vertices(the_graph). P(L,s)
P(L @ [i],dfs(the_obj;s;i))
6.
n:
7.
L:
Vertices(the_graph) List
8.
L1:Vertices(the_graph) List. ||L1|| < ||L||
P(L1,list_accum(s,i.dfs(the_obj;s;i);nil;L1))
9.
L = nil
10.
x:
Vertices(the_graph)
11.
L':
Vertices(the_graph) List
12.
L = (L' @ [x])
P(L' @ [x],list_accum(s,i.dfs(the_obj;s;i);nil;L' @ [x]))
By:
(InstHyp [L'] -5) THENA ((Auto THEN (HypSubst -1 0)) THEN (RWO
Thm*
as,bs:T List. ||as @ bs|| = ||as||+||bs||
0))
Generated subgoal:
1
13.
P(L',list_accum(s,i.dfs(the_obj;s;i);nil;L'))
P(L' @ [x],list_accum(s,i.dfs(the_obj;s;i);nil;L' @ [x]))
1
step
About:
(3steps total)
PrintForm
Definitions
Lemmas
graph
1
3
Sections
Graphs
Doc