
theorem Th23:
  for L be complete Boolean LATTICE for X be Subset of L for x be
Element of L holds x "/\" sup X = "\/"({x"/\"y where y is Element of L: y in X}
  ,L)
proof
  let L be complete Boolean LATTICE;
  let X be Subset of L;
  let x be Element of L;
  for y be Element of L holds y "/\" is lower_adjoint by WAYBEL_1:def 19;
  hence thesis by WAYBEL_1:64;
end;
