
theorem
  for G1, G2 being non-multi _Graph, f being PVertexMapping of G1, G2
  st f is total one-to-one holds PVM2PGM(f) is weak_SG-embedding
proof
  let G1, G2 be non-multi _Graph, f being PVertexMapping of G1, G2;
  assume f is total one-to-one;
  then PVM2PGM(f) is total one-to-one by Th32, Th34;
  hence thesis;
end;
