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:];

theorem Th45: :: (19)
  X misses R~.:Y iff Y misses R.:X
proof
  X meets R~.:Y iff ex x,y being set st x in X & y in Y & x in Im(R~,y)
  by Th43;
  hence thesis by Th44;
end;
