The poset $P$ is a lower semilattice if every pair of vertices has a unique greatest lower bound (meet).
Clearly, the $n$ chain and the $n$ booleanLattice are lower semilattices.
i1 : n = 4; |
i2 : isLowerSemilattice chain n o2 = true |
i3 : B = booleanLattice n; |
i4 : isLowerSemilattice B o4 = true |
The middle ranks of the $n$ booleanLattice are not lower semilattices.
i5 : isLowerSemilattice flagPoset(B, {1,2,3}) o5 = false |
However, the lower ranks of the $n$ booleanLattice are non-lattice lower semilattices.
i6 : B' = flagPoset(B, {0,1,2,3}); |
i7 : isLattice B' o7 = false |
i8 : isLowerSemilattice B' o8 = true |
The object isLowerSemilattice is a method function.