Let H be a non empty subset of the carrier of U 0 and given o . For every subalgebra U 1 of U 0 holds the carrier of U 1 the carrier of U 0 . Let U 0 be a universal algebra with constants. One can verify that every subalgebra of U 0 has constants. Let us consider U 0 .
H is non empty.
Then l 1 l 2 if and only if the carrier of U 1 the carrier of U 3 . Then l 1 l 2 if and only if U 1 is a subalgebra of U 3 . For every strict universal algebra U 0 with constants holds the lattice of subalgebras of U 0 is bounded. Let U 0 be a strict universal algebra with constants. Note that the lattice of subalgebras of U 0 is bounded.