reserve G for _Graph;

theorem
  VertexAdjSymRel(G) = ((the_Source_of G qua Relation)~ * (the_Target_of G))
    \/ ((the_Target_of G qua Relation)~ * (the_Source_of G))
proof
  set S = the_Source_of G, T = the_Target_of G;
  thus VertexAdjSymRel(G)
     = ((S qua Relation)~ * T) \/ ((T qua Relation)~ * ((S qua Relation)~~))
      by RELAT_1:35
    .= ((S qua Relation)~ * T) \/ ((T qua Relation)~ * S);
end;
