The rigidification of a symmetric formula of orbit size $< n.choose κ$ has support size $≤ κ - 1$ by the support theorem, and support depth $≤ 2κ$: along any path, support-changing wires are moved by stabilisers so that each adds a new point to the union of supports; lifting to the formula, where non-input gates have unique parents, bounds both sides of this union by $κ - 1$ while the path ends in a non-input gate.