reserve X, Y for non empty set;
reserve X for non empty set;
reserve R for RMembership_Func of X,X;

theorem Th33:
  for R being complete Heyting LATTICE, X being Subset of R, y be
Element of R holds y "/\" "\/"(X,R) = "\/"({y "/\" x where x is Element of R: x
  in X},R)
proof
  let R be complete Heyting LATTICE, X be Subset of R, y be Element of R;
  for z being Element of R holds z "/\" is lower_adjoint by WAYBEL_1:def 19;
  hence thesis by WAYBEL_1:64;
end;
