
theorem Th82:
  for G1, G2 being _Graph, F being one-to-one PGraphMapping of G1, G2,
    H being Subgraph of G1 holds (F|H)" = H |` (F")
proof
  let G1, G2 be _Graph, F be one-to-one PGraphMapping of G1, G2;
  let H be Subgraph of G1;
  reconsider f = F_V, g = F_E as one-to-one Function;
  thus (F|H)"
     = [ (the_Vertices_of H) |` (f"), (g | the_Edges_of H)"] by GLIB_009:5
    .= H |` (F") by GLIB_009:5;
end;
