0PB5 Lemma 7.4.16. Let I′I^{\prime} be a subset of II such that I−I′⊂ZoI-I^{\prime}\subset Z_{o} and θi=id\theta_{i}=\operatorname{id}\nolimits for i∈I−I′i\in I-I^{\prime}. We have D(θ|I′)⊂D(θ)D(\theta_{|I^{\prime}})\subset D(\theta).
0PB6 Proof. We have L(θ|I′)⊂L(θ)L(\theta_{|I^{\prime}})\subset L(\theta) and Lemma 7.4.15 shows that D(θ|I′)⊂D(θ)D(\theta_{|I^{\prime}})\subset D(\theta). ∎