
theorem Th34:
  for G1, G2 being _Graph, F being PGraphMapping of G1, G2 st F is total
  for v being Vertex of G1 holds F_V.v is Vertex of G2
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2;
  assume A1: F is total;
  let v be Vertex of G1;
  F_V.v in rng F_V by A1, FUNCT_1:3;
  hence thesis;
end;
