
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.minDegree() = G2.minDegree() or
    G1.minDegree() = min(v.degree(),w.degree()) + 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;
  min(v.degree(),w.degree()) + 1 = (v.degree() /\ w.degree()) +` 1;
  hence thesis by Th70;
end;
