
theorem Th93:
  for G1, G2 being _Graph, F0 being PGraphMapping of G1, G2
  st F0_E is one-to-one
  ex E being Subset of the_Edges_of G2 st
  for G3 being reverseEdgeDirections of G2, E
  ex F being PGraphMapping of G1, G3 st F = F0 & F is directed &
    (F0 is weak_SG-embedding implies F is weak_SG-embedding) &
    (F0 is strong_SG-embedding implies F is strong_SG-embedding) &
    (F0 is isomorphism implies F is isomorphism)
proof
  let G1, G2 be _Graph, F0 be PGraphMapping of G1, G2;
  assume F0_E is one-to-one;
  then consider E being Subset of the_Edges_of G2 such that
    A1: for G3 being reverseEdgeDirections of G2, E
      ex F being PGraphMapping of G1, G3 st F = F0 & F is directed &
        (F0 is non empty  implies F is non empty) &
        (F0 is total implies F is total) &
        (F0 is one-to-one implies F is one-to-one) &
        (F0 is onto implies F is onto) &
        (F0 is semi-continuous implies F is semi-continuous) &
        (F0 is continuous implies F is continuous) by Th92;
  take E;
  let G3 be reverseEdgeDirections of G2, E;
  consider F being PGraphMapping of G1, G3 such that
    A2: F = F0 & F is directed and
    F0 is non empty  implies F is non empty and
    A3: F0 is total implies F is total and
    A4: F0 is one-to-one implies F is one-to-one and
    A5: F0 is onto implies F is onto and
    F0 is semi-continuous implies F is semi-continuous and
    A6: F0 is continuous implies F is continuous by A1;
  take F;
  thus F = F0 & F is directed by A2;
  thus thesis by A3, A4, A5, A6;
end;
