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Proof step 2 from proof idset-mapped-pebs-write-unused (previous step)

wlar[n] = wl-entry(m, stat), n < # wlar, id○(apebs, apebs0, n), valid-ebatbl(apebs, wlar, vols, n0) ⊦ stat = used, id(apebs, apebs0, mapped-pebs(vols))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# 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

Rule argument

Additional information

Used simplifier rules: valid-ebatbl: ⊦ valid-ebatbl(apebs, wlar, vols, n0) ↔ (∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ n < # wlar ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ n0);%id-set: ⊦ id(apebs0, apebs1, ns) ↔ # apebs0 = # apebs1 ∧ (∀ n. n ∈ ns ∧ n < # apebs0 ∧ n < # apebs1 → apebs0[n] = apebs1[n]);%mapped-pebs: ⊦ n ∈ mapped-pebs(vols) ↔ (∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ );%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)%idexcept-size: ⊦ id○(apebs, apebs0, n) → # apebs = # apebs0; (forward) from specification array-copy[apebs]%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic