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Proof step 3 from proof mapped-pebs-add-empty-vol (previous step)

⊦ mapped-pebs(vols[v, fill(mkebatbl(n), unmapped)]) = mapped-pebs(vols), v ∈ vols

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0)
Proof step 5:
⊦ v ∈ vols, ∀ n0. n0 ∈ mapped-pebs(vols[v, fill(mkebatbl(n), unmapped)]) ↔ n0 ∈ mapped-pebs(vols)

Rule argument

spec: set-basic, inst: nat-set name: Extension seq: ⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0) subst: [ns0, ns] → [mapped-pebs(vols), mapped-pebs(vols[v, fill(mkebatbl(n), unmapped)])] flags: <all paths>

Additional information

Used terms: mapped-pebs(vols), mapped-pebs(vols[v, fill(mkebatbl(n), unmapped)])