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Proof step 109 from proof refine-read (previous step)

# vols[v] = # avols[v], # apebs = # wlar, apebs[n1] = mkpeb(aehdr, avhdr, buf1, m, boolvar), vols[v][vtblpnum5] = ⌜n1⌝ , avols[v][vtblpnum5] = mapped(buf1, m0), vtblpnum5 < # avols[v], bflipset-cons(bflipset, wlar), ebm-cons(avols), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum3), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum3), valid-wl(apebs, wlar), v ∈ vols, v ∈ avols, m ≤ m0, n0 + n ≤ # buf2, vtblpnum4 + n ≤ LEB_SIZE ⊦ VTBL_VOLID ∈ vols, n1 < # wlar ∧ ¬ boolvar

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 110:
⊦ 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)
Proof step 111:
# apebs = # wlar, # vols[v] = # avols[v], avols[v][vtblpnum5] = mapped(buf1, m0), vols[v][vtblpnum5] = ⌜n1⌝ , apebs[n1] = mkpeb(aehdr, avhdr, buf1, m, boolvar), vtblpnum5 < # avols[v], bflipset-cons(bflipset, wlar), ebm-cons(avols), ubi-io-inv(apebs), unique-sqns(apebs), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum3), valid-wl(apebs, wlar), v ∈ avols, v ∈ vols, vtblpnum4 + n ≤ LEB_SIZE, n0 + n ≤ # buf2, m ≤ m0, ∀ 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 ≠ vtblpnum3 ⊦ VTBL_VOLID ∈ vols, n1 < # wlar ∧ ¬ boolvar

Rule argument

spec: ubi-base name: valid-ebatbl seq: ⊦ 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) subst: [n0, vols, wlar, apebs] → [vtblpnum3, vols, wlar, apebs] flags: <all paths>

Additional information

Used terms: vtblpnum3, vols, wlar, apebs