
theorem
  for G1, G2 being _Graph, F being PGraphMapping of G1, G2
  holds F * id G1 = F & (id G2) * F = F
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2;
  A1: dom F_V c= the_Vertices_of G1 & dom F_E c= the_Edges_of G1;
  thus F * id G1 = [F_V, F_E * id the_Edges_of G1] by A1, RELAT_1:51
    .= [F_V, F_E] by A1, RELAT_1:51
    .= F;
  A2: rng F_V c= the_Vertices_of G2 & rng F_E c= the_Edges_of G2;
  thus (id G2) * F = [F_V, (id the_Edges_of G2) * F_E] by A2, RELAT_1:53
    .= [F_V, F_E] by A2, RELAT_1:53
    .= F;
end;
