
theorem Th142:
  for G1, G2 being _Graph, E1, E2 being set
  for G3 being reverseEdgeDirections of G1, E1
  for G4 being reverseEdgeDirections of G2, E2
  for F0 being PGraphMapping of G1, G2
  ex F being PGraphMapping of G3, G4 st F = F0 &
    (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, E1, E2 be set;
  let G3 be reverseEdgeDirections of G1, E1;
  let G4 be reverseEdgeDirections of G2, E2;
  let F0 be PGraphMapping of G1, G2;
  consider F being PGraphMapping of G3, G4 such that
    A1: F = F0 and
    F0 is non empty  implies F is non empty and
    A2: F0 is total implies F is total and
    A3: F0 is onto implies F is onto and
    A4: F0 is one-to-one implies F is one-to-one and
    F0 is semi-continuous implies F is semi-continuous and
    A5: F0 is continuous implies F is continuous by Th141;
  take F;
  thus F = F0 by A1;
  thus F0 is weak_SG-embedding implies F is weak_SG-embedding by A2, A4;
  thus F0 is strong_SG-embedding implies F is strong_SG-embedding
    by A2, A4, A5;
  thus F0 is isomorphism implies F is isomorphism by A2, A3, A4;
end;
