
theorem
  for G1, G2 being _finite _Graph, F being PGraphMapping of G1, G2
  st F is strong_SG-embedding
  holds (ex F0 being PGraphMapping of G1, G2 st F0 is isomorphism)
    implies F is isomorphism
proof
  let G1, G2 be _finite _Graph, F be PGraphMapping of G1, G2;
  assume A1: F is strong_SG-embedding;
  given F0 being PGraphMapping of G1, G2 such that
    A2: F0 is isomorphism;
  G1.order() = G2.order() & G1.size() = G2.size() by A2, Th84;
  hence thesis by A1, Th51;
end;
