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Proof step 3 from proof mapped-pebs-remap (previous step)

vols[v][m] = ⌜n0⌝ , m < # vols[v], v ∈ vols, ∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ m0 ⊦ mapped-pebs(vols[v, vols[v][m, ⌜n1⌝ ]]) = (mapped-pebs(vols) -- n0) ++ n1

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:
vols[v][m] = ⌜n0⌝ , m < # vols[v], v ∈ vols, ∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ m0 ⊦ ∀ n. n ∈ mapped-pebs(vols[v, vols[v][m, ⌜n1⌝ ]]) ↔ n ∈ (mapped-pebs(vols) -- n0) ++ n1

Rule argument

spec: set-basic, inst: nat-set name: Extension seq: ⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0) subst: [ns0, ns] → [(mapped-pebs(vols) -- n0) ++ n1, mapped-pebs(vols[v, vols[v][m, ⌜n1⌝ ]])] flags: <all paths>

Additional information

Used terms: (mapped-pebs(vols) -- n0) ++ n1, mapped-pebs(vols[v, vols[v][m, ⌜n1⌝ ]])