
theorem
  for G being _Graph, v being Vertex of G, C being inducedSubgraph of G, {v}
  st v is isolated holds C is Component of G
proof
  let G be _Graph, v be Vertex of G, C be inducedSubgraph of G, {v};
  assume v is isolated;
  then {v} = G.reachableFrom(v) by Th55;
  hence thesis;
end;
