
theorem
  for G1, G2, G3 being _Graph, F1 being PGraphMapping of G1, G2,
    F2 being PGraphMapping of G2, G3, H being Subgraph of G3
  holds (H|`F2) * F1 = H |` (F2*F1)
proof
  let G1, G2, G3 be _Graph;
  let F1 be PGraphMapping of G1, G2;
  let F2 be PGraphMapping of G2, G3;
  let H be Subgraph of G3;
  thus (H|`F2) * F1
     = [ (the_Vertices_of H) |` (F2_V * F1_V),
      ((the_Edges_of H) |` F2_E) * F1_E ] by RELAT_1:108
    .= H |` (F2*F1) by RELAT_1:108;
end;
