
theorem
  for G1, G2, G3, G4 being _Graph, F1 being PGraphMapping of G1, G2,
    F2 being PGraphMapping of G2, G3, F3 being PGraphMapping of G3, G4
  holds F3 * (F2 * F1) = (F3 * F2) * F1
proof
  let G1, G2, G3, G4 be _Graph, F1 be PGraphMapping of G1, G2,
    F2 be PGraphMapping of G2, G3, F3 be PGraphMapping of G3, G4;
  thus F3 * (F2 * F1)
     = [(F3_V * F2_V) * F1_V, F3_E * (F2_E * F1_E)] by RELAT_1:36
    .= (F3 * F2) * F1 by RELAT_1:36;
end;
