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 Th59: :: (24.3)
  (R`)~ = (R~)`
proof
  (R`)~ = ([:A,B:])~ \ R~ by RELAT_1:24
    .= (R~)` by SYSREL:5;
  hence thesis;
end;
