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Proof step 445 from proof refine-write (previous step)

# apebs = # wlar, v ∈ vols ↔ v ∈ avols, 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, 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, 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 446:
# vols[v] = # avols[v], # apebs = # wlar, vols[v][vtblpnum3] = ⌜n1⌝ , apebs[n1] = mkpeb(aehdr, avhdr, buf0, m, boolvar), avols[v][vtblpnum3].mapped?, avols[v][vtblpnum3].fill < m, n1 < # wlar, vtblpnum3 < # avols[v], vtblpnum5 < m, bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), is-aligned(vtblpnum5, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf0, m, boolvar)), 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, ∀ m. m < # avols[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

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%ubi-io-inv-fwd: n < # apebs ⊦ apebs[n] = apeb ∧ ubi-io-inv(apebs) → ubi-io-peb-inv(apeb); (forward) from specification ubi-asm% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)