Update instruction_lookups.md

book/src/how/instruction_lookups.md

@@ -52,9 +52,9 @@ $$
 
 
 ## Subtable Flags
-`TODO`
+
 - We then use memory checking to determine that each of the memories $E_i$ is well formed
 - At a given step of the CPU only a single instruction will be used, that means that only that instruction's subtables will be used. For the rest of the memories we insert a no_op with (a, v) = 0. In order to make the GKR trees cheaper to compute and sumcheck we'll add a single additional layer to the GKR tree. During this layer we'll "toggle" each of the GKR leaves to "1" in the case that it is an unused step of the CPU. This will make the binary tree of multiplication gates cheaper. We'll toggle based on a new flags polynomial called $subtable-flags_f$ which is the sum of all of the $instruction-flags_f$ used in the instruction collation above.
 - The function to compute each of the leaves becomes $leaf[i] = \text{subtable-flags}[i] \cdot \text{fingerprint}[i] + (1 - \text{subtable-flags}[i])$
 
-  See the documentation on how Jolt leverages [sparse-constraint-systems](sparse-constraint-systems.md) for further details on subtagle flags and how they are used in Jolt. 
+See the documentation on how Jolt leverages [sparse-constraint-systems](sparse-constraint-systems.md) for further details on subtagle flags and how they are used in Jolt.