reserve Y for non empty set,
  a for Function of Y,BOOLEAN,
  G for Subset of PARTITIONS(Y),
  P,Q for a_partition of Y;
reserve x,y,z for set,
  S, X for non empty set,
  R for Relation of X;

theorem
  field id X = X
proof
  dom id X = X & rng id X = X;
  then field id X = X \/ X by RELAT_1:def 6;
  hence thesis;
end;
