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
  R is_reflexive_in X implies R is reflexive & field R = X
by Th9;
