graph 1 3 Sections Graphs Doc

Def non-trivial-loop-free(G) == i:Vertices(G). non-trivial-loop(G;i)

is mentioned by

Thm* For any graph the_obj:GraphObject(the_graph), L:V List. (i:V. (i L)) (non-trivial-loop-free(the_graph) topsortedl(the_graph;L;topsortl(the_obj;L))) & (i:V. (i topsortl(the_obj;L))) & no_repeats(V;topsortl(the_obj;L))[topsortl-properties]
Thm* For any graph the_obj:GraphObject(the_graph). L:V List. (non-trivial-loop-free(the_graph) topsorted(the_graph;L)) & (i:V. (i L)) & no_repeats(V;L)[topsort-exists]
Thm* For any graph the_obj:GraphObject(the_graph). (non-trivial-loop-free(the_graph) topsorted(the_graph;topsort(the_obj))) & (i:V. (i topsort(the_obj))) & no_repeats(V;topsort(the_obj))[topsort-properties]

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graph 1 3 Sections Graphs Doc