theorem Th37:
  c is Chain of AddNewEdge(v1, v2)
proof
  set G9 = AddNewEdge(v1, v2);
  consider p being FinSequence of the carrier of G such that
A1: p is_vertex_seq_of c by GRAPH_2:33;
  c is FinSequence of the carrier' of G by MSSCYC_1:def 1;
  then
A2: rng c c= the carrier' of G by FINSEQ_1:def 4;
  the carrier' of G9 = (the carrier' of G) \/ {the carrier' of G} by Def7;
  then the carrier' of G c= the carrier' of G9 by XBOOLE_1:7;
  then rng c c= the carrier' of G9 by A2;
  hence c is FinSequence of the carrier' of G9 by FINSEQ_1:def 4;
  reconsider p9 = p as FinSequence of the carrier of G9 by Def7;
  take p9;
  thus thesis by A1,Th36;
end;
