
theorem
  for G1, G2 being _Graph, F being PGraphMapping of G1, G2,
    H1 being Subgraph of G1, H2 being Subgraph of G2
  holds (H2|`F)|H1 = H2|`(F|H1)
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2;
  let H1 be Subgraph of G1, H2 be Subgraph of G2;
  thus (H2|`F)|H1
     = [ (the_Vertices_of H2) |` (F_V | the_Vertices_of H1),
      ((the_Edges_of H2) |` F_E) | the_Edges_of H1 ] by RELAT_1:109
    .= H2|`(F|H1) by RELAT_1:109;
end;
