reserve x,y for object,X,Y,A,B,C,M for set;
reserve P,Q,R,R1,R2 for Relation;
reserve X,X1,X2 for Subset of A;
reserve Y for Subset of B;
reserve R,R1,R2 for Subset of [:A,B:];
reserve FR for Subset-Family of [:A,B:];
reserve R for Relation of A,B;
reserve S for Relation of B,C;

theorem :: (21)
  R.:(X`) c= Y` iff R~.:Y c= X
proof
  X` misses R~.:Y iff Y misses R.:(X`) by Th45;
  hence thesis by SUBSET_1:23,24;
end;
