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Proof step 442 from proof refine-write (previous step)

# apebs = # wlar, vols[v][vtblpnum3] = ⌜n1⌝ , apebs[n1] = mkpeb(aehdr, avhdr, buf0, m, boolvar), avols[v][vtblpnum3].mapped?, n1 < # wlar, vtblpnum3 < # avols[v], vtblpnum3 < # vols[v], vtblpnum5 < m, avols[v][vtblpnum3].fill < m, abs(avols, apebs, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), is-aligned(vtblpnum5, EB_PAGE_SIZE), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs, wlar), v ∈ avols, v ∈ vols, avols[v][vtblpnum3].fill ≤ vtblpnum5, n + n0 ≤ # buf, vtblpnum5 + n ≤ LEB_SIZE ⊦ VTBL_VOLID ∈ vols

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 443:
⊦ abs(avols, apebs, vols, q) ↔ (∀ v. (v ∈ vols ↔ v ∈ avols) ∧ ( v ∈ vols → # vols[v] = # avols[v] ∧ (∀ m. m < # vols[v] → (vols[v][m] = unmapped → ¬ avols[v][m].mapped?) ∧ ( vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = apebs[vols[v][m].pnum].data ∧ apebs[vols[v][m].pnum].fill ≤ avols[v][m].fill) ∧ (avols[v][m] = erased → ¬ v × m ∈ q))))
Proof step 444:
# apebs = # wlar, apebs[n1] = mkpeb(aehdr, avhdr, buf0, m, boolvar), vols[v][vtblpnum3] = ⌜n1⌝ , avols[v][vtblpnum3].mapped?, avols[v][vtblpnum3].fill < m, vtblpnum5 < m, vtblpnum3 < # vols[v], vtblpnum3 < # avols[v], n1 < # wlar, bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(vtblpnum5, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs, wlar), v ∈ vols, v ∈ avols, vtblpnum5 + n ≤ LEB_SIZE, n + n0 ≤ # buf, avols[v][vtblpnum3].fill ≤ vtblpnum5, ∀ v. (v ∈ vols ↔ v ∈ avols) ∧ ( v ∈ vols → # vols[v] = # avols[v] ∧ (∀ m. m < # vols[v] → (vols[v][m] = unmapped → ¬ avols[v][m].mapped?) ∧ ( vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = apebs[vols[v][m].pnum].data ∧ apebs[vols[v][m].pnum].fill ≤ avols[v][m].fill) ∧ (avols[v][m] = erased → ¬ v × m ∈ q))) ⊦ VTBL_VOLID ∈ vols

Rule argument

spec: ubi-abs name: abs-def seq: ⊦ abs(avols, apebs, vols, q) ↔ (∀ v. (v ∈ vols ↔ v ∈ avols) ∧ ( v ∈ vols → # vols[v] = # avols[v] ∧ (∀ m. m < # vols[v] → ( vols[v][m] = unmapped → ¬ avols[v][m].mapped?) ∧ ( vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = apebs[vols[v][m].pnum].data ∧ apebs[vols[v][m].pnum].fill ≤ avols[v][m].fill) ∧ (avols[v][m] = erased → ¬ v × m ∈ q)))) subst: [q, vols, apebs, avols] → [q, vols, apebs, avols] flags: <all paths>

Additional information

Used terms: q, vols, apebs, avols