lut Y22 checks if the a[1:0] is greater than b[1:0].
If a[1:0] > b[1:0], the result is taken from this test: a[3:2] >= b[3:2].
If a[1:0] <= b[1:0], the result is taken from this test: a[3:2] > b[3:2].
The test is for A to be larger than B, for A to win the full comparison.
So if A wins the low bits test, the A high bits must just not lose their test for A to win the full comparison.
But if A loses the low bits test, the A high bits do have to win for A to win the full comparison.