
theorem Th139:
  for G1 being _Graph, G2 being DSimpleGraph of G1
  for v1 being Vertex of G1, v2 being Vertex of G2 st v1 = v2
  holds G1.reachableFrom(v1) = G2.reachableFrom(v2)
proof
  let G1 be _Graph, G2 be DSimpleGraph of G1;
  for W1 being Walk of G1 ex W2 being Walk of G2
    st W2 is_Walk_from W1.first(),W1.last() by Th137;
  hence for v1 being Vertex of G1, v2 being Vertex of G2 st v1 = v2
    holds G1.reachableFrom(v1) = G2.reachableFrom(v2) by Th35;
end;
