
theorem
  for G2 being locally-finite _Graph, v,w being Vertex of G2,e being object
  for G1 being addEdge of G2,v,e,w st v <> w holds
    G1.minOutDegree() = G2.minOutDegree() or
    G1.minOutDegree() = v.outDegree() + 1
proof
  let G2 be locally-finite _Graph, v,w be Vertex of G2, e be object;
  let G1 be addEdge of G2,v,e,w;
  v.outDegree() +` 1 = v.outDegree() +` 1;
  hence thesis by Th72;
end;
