Albert Lai
Walking down College Street,
Looking for a dinner treat,
I contemplated an evasive stud,
The lattice-theoretic cross product.
Let {(a_i, b_i)} be a subset of LxM
Whose join is called (l,m).
Choose irredundant {a_j} that forms l in L
And irredundant {b_k} that forms m in M.
So {(a_j,b_j)}U{(a_k,b_k)} joins to (l,m),
And this bounds the breadth of LxM.
But {(a_j,b_j)} is under the breadth of L,
And {(a_k,b_k)} stays below the breadth of M!
To see that this bound is an equation,
You just have to stretch your imagination.
Now if I work more on the join-irredundant,
I may as well join the math department.