
theorem
  for G1, G2 being _Graph, G3 being Component of G1 st G1 == G2
  holds G3 is Component of G2
proof
  let G1, G2 be _Graph, G3 be Component of G1;
  assume A1: G1 == G2;
  now
    given G4 being connected Subgraph of G2 such that
      A2: G3 c< G4;
    G4 is Subgraph of G1 by A1, GLIB_000:91;
    hence contradiction by A2, GLIB_002:def 7;
  end;
  hence thesis by A1, GLIB_000:91, GLIB_002:def 7;
end;
