
theorem Th32:
  for G1, G2 being _Graph, F being PGraphMapping of G1, G2
  st F is weak_SG-embedding & G2 is locally-finite holds G1 is locally-finite
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2;
  assume A1: F is weak_SG-embedding & G2 is locally-finite;
  now
    let v be Vertex of G1;
    v.degree() c= (F_V/.v).degree() by A1, GLIBPRE0:89;
    hence v.degree() is finite by A1;
  end;
  hence thesis by Th23;
end;
