18 Now, ψ must be a reducing substitution for the simulated derivation, because all instantiated rules in IR root are appropriately instantiated and pair-wise compatible and because condition (iic) of Definition 16 ensures that rules that are not self-compatible can only be used once for licensing the Cat projection.
because of Lemma 2, the derivation in G F simulates a derivation of an f-description in G that ψ reduces to the equivalent description provided by IR root .