
theorem
  for G being EGraph, e,x being set st e in the_Edges_of G holds e in G
  .labelEdge(e,x).labeledE()
proof
  let G be EGraph, e,x be set;
  assume e in the_Edges_of G;
  then
A1: G.labelEdge(e,x).labeledE() = G.labeledE() \/ {e} by Th45;
  e in {e} by TARSKI:def 1;
  hence thesis by A1,XBOOLE_0:def 3;
end;
