
theorem
  for G being EGraph, e,x being set st e in the_Edges_of G holds G
  .labeledE() c= G.labelEdge(e,x).labeledE()
proof
  let G be EGraph, e,x be set;
  assume e in the_Edges_of G;
  then G.labelEdge(e,x).labeledE() = G.labeledE() \/ {e} by Th45;
  hence thesis by XBOOLE_1:7;
end;
