theorem Th136:
  for G being _Graph holds G is loopless iff
  for v being object holds not ex e being object st e DJoins v,v,G
proof
  let G be _Graph;
  thus G is loopless implies
   for v being object holds not ex e being object st e DJoins v,v,G;
  assume A3: for v being object holds not ex e being object st e DJoins v,v,G;
  for v being object holds not ex e being object st e Joins v,v,G
  proof
    let v be object;
    given e being object such that
      A4: e Joins v,v,G;
    e DJoins v,v,G by A4;
    hence contradiction by A3;
  end;
  hence thesis by Th18;
end;
