
theorem Th24:
  for G being _Graph, C being a_partition of the_Vertices_of G,
    v being Vertex of G
  st C = G.componentSet() holds EqClass(v,C) = G.reachableFrom(v)
proof
  let G be _Graph, C be a_partition of the_Vertices_of G, v be Vertex of G;
  assume A1: C = G.componentSet();
  EqClass(v,C) in C by EQREL_1:def 6;
  then consider w being Vertex of G such that
    A2: EqClass(v,C) = G.reachableFrom(w) by A1, GLIB_002:def 8;
  v in EqClass(v,C) by EQREL_1:def 6;
  hence thesis by A2, GLIB_002:12;
end;
