
theorem
  for G1, G2, G3 being _Graph, F1 being PGraphMapping of G1, G2,
    F2 being PGraphMapping of G2, G3, H being Subgraph of G1
  holds F2 * (F1|H) = (F2*F1) | H
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 G1;
  thus F2 * (F1|H)
     = [ (F2_V * F1_V) | the_Vertices_of H, F2_E * (F1_E | the_Edges_of H) ]
      by RELAT_1:83
    .= (F2*F1) | H by RELAT_1:83;
end;
