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Proof step 3 from proof idset-mapped-pebs-write-unused (previous step)

# apebs = # apebs0, vols[v][m0] = ⌜n1⌝ , wlar[n] = wl-entry(m, stat), n1 < # apebs0, m0 < # vols[v], n < # wlar, id○(apebs, apebs0, n), v ∈ vols, ∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs0 ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0 ⊦ apebs[n1] = apebs0[n1], stat = used

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ id○(apebs, apebs0, n) ↔ # apebs = # apebs0 ∧ (∀ m. m < # apebs ∧ m ≠ n → apebs[m] = apebs0[m])
Proof step 5:
# apebs = # apebs0, wlar[n] = wl-entry(m, stat), vols[v][m0] = ⌜n1⌝ , n < # wlar, m0 < # vols[v], n1 < # apebs0, v ∈ vols, ∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs0 ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0, ∀ m. m < # apebs ∧ m ≠ n → apebs[m] = apebs0[m] ⊦ apebs[n1] = apebs0[n1], stat = used

Rule argument

spec: array-copy, inst: apebs name: Idexcept seq: ⊦ id○(apebs, apebs0, n) ↔ # apebs = # apebs0 ∧ (∀ m. m < # apebs ∧ m ≠ n → apebs[m] = apebs0[m]) subst: [n, apebs0, apebs] → [n, apebs0, apebs] flags: <all paths>

Additional information

Used terms: n, apebs0, apebs