reserve G for Graph,
  v, v1, v2 for Vertex of G,
  c for Chain of G,
  p, p1, p2 for Path of G,
  vs, vs1, vs2 for FinSequence of the carrier of G,
  e, X for set,
  n, m for Nat;
reserve G for finite Graph,
  v for Vertex of G,
  c for Chain of G,
  vs for FinSequence of the carrier of G,
  X1, X2 for set;

theorem Th25:
  Degree(v, X) <> 0 implies Edges_At(v, X) is non empty
proof
  assume
A1: Degree(v, X) <> 0;
  assume
A2: not thesis;
  then Edges_In(v, X) = {};
  hence contradiction by A1,A2;
end;
