(47steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc

At: topsortl-properties 1
1. the_graph: Graph
2. the_obj: GraphObject(the_graph)
3. L: Vertices(the_graph) List
4. i:Vertices(the_graph). (i L)
5. paren(Vertices(the_graph);dfsl(the_obj;L))
6. no_repeats(Vertices(the_graph)+Vertices(the_graph);dfsl(the_obj;L))
7. dfsl-traversal(the_graph;L;dfsl(the_obj;L))
8. i:Vertices(the_graph). (i L) (inr(i) dfsl(the_obj;L)) & (inl(i) dfsl(the_obj;L))
non-trivial-loop-free(the_graph) topsortedl(the_graph;L;topsortl(the_obj;L))
By:
Analyze 0
THEN
Assert (L1,L2:Vertices(the_graph) List. L = (L1 @ L2) (s1,s2:Vertices(the_graph) List. topsortl(the_obj;L) = (s2 @ s1) & (j:Vertices(the_graph). ((j s1) L1-the_graph- > *j) & ((j s2) L2-the_graph- > *j & L1-the_graph- > *j))))
Generated subgoals:

19. non-trivial-loop-free(the_graph)
L1,L2:Vertices(the_graph) List. L = (L1 @ L2) (s1,s2:Vertices(the_graph) List. topsortl(the_obj;L) = (s2 @ s1) & (j:Vertices(the_graph). ((j s1) L1-the_graph- > *j) & ((j s2) L2-the_graph- > *j & L1-the_graph- > *j)))		1 step
 
29. non-trivial-loop-free(the_graph)
10. L1,L2:Vertices(the_graph) List. L = (L1 @ L2) (s1,s2:Vertices(the_graph) List. topsortl(the_obj;L) = (s2 @ s1) & (j:Vertices(the_graph). ((j s1) L1-the_graph- > *j) & ((j s2) L2-the_graph- > *j & L1-the_graph- > *j)))
topsortedl(the_graph;L;topsortl(the_obj;L))		41 steps

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listunioninlinrequalimpliesandallexists

(47steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc