Oh, hm. So of course we can combine the two true statements into a single statement that says that their (full) sequence of exponents must be weakly decreasing.

For some reason when you wrote that I made the inference that this sequence of weakly decreasing sequences is itself increasing! (In the pointwise partial order, or you can think of all this as living in Young's lattice. :) ) But as your example shows that's not true. Huh...