reserve A for set,
  C for non empty set,
  B for Subset of A,
  x for Element of A,
  f,g for Function of A,C;
reserve B for Element of Fin A;
reserve L for non empty LattStr,
  a,b,c for Element of L;
reserve L for Lattice;
reserve a,b,c,u,v for Element of L;

theorem Th27:
  the L_meet of L absorbs the L_join of L
proof
  let x,y be Element of L;
  thus (the L_meet of L).(x,(the L_join of L).(x,y)) = x "/\"(x "\/" y)
    .= x by LATTICES:def 9;
end;
