
theorem Th32:
  for G being EGraph, e,x being set st e in the_Edges_of G holds
  the_ELabel_of G.labelEdge(e,x) = the_ELabel_of G +* (e .--> x)
proof
  let G be EGraph, e,x be set;
  assume e in the_Edges_of G;
  then the_ELabel_of G.labelEdge(e,x) = G.set(ELabelSelector, the_ELabel_of G
  +* (e .-->x)).ELabelSelector by Def21;
  hence thesis by GLIB_000:8;
end;
