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Proof step 440 from proof refine-write (previous step)

# apebs = # wlar, buf0 = buf, vtblpnum = vtblpnum4, vtblpnum0 = EB_PAGE_SIZE, vtblpnum1 = vtblpnum5, vtblpnum2 = vtblpnum3, vtblpnum3 < # avols[v], abs(avols, apebs, vols, q), 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 ∈ avols, vtblpnum5 + n ≤ LEB_SIZE, n + n0 ≤ # buf, avols[v][vtblpnum3].mapped? → avols[v][vtblpnum3].fill ≤ vtblpnum5, v ∈ vols → v ∈ vols ∧ ( vtblpnum2 < # vols[v] → vtblpnum1 + n ≤ LEB_SIZE → n0 + n ≤ # buf0 → is-aligned(n, EB_PAGE_SIZE) → is-aligned(vtblpnum1, EB_PAGE_SIZE) → (vtblpnum2 < # vols[v] ∧ v ∈ vols) ∧ ( vols[v][vtblpnum2] ≠ unmapped → vols[v][vtblpnum2].pnum < # apebs ∧ vols[v][vtblpnum2] ≠ unmapped ∧ vtblpnum2 < # vols[v] ∧ v ∈ vols)) ⊦ VTBL_VOLID ∈ vols, v ∈ vols ∧ vtblpnum2 < # vols[v] ∧ vtblpnum1 + n ≤ LEB_SIZE ∧ n0 + n ≤ # buf0 ∧ is-aligned(n, EB_PAGE_SIZE) ∧ is-aligned(vtblpnum1, EB_PAGE_SIZE) ∧ (vols[v][vtblpnum2] ≠ unmapped → apebs[vols[v][vtblpnum2].pnum].fill ≤ vtblpnum1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 441:
# apebs = # wlar, vols[v][vtblpnum3] = ⌜n1⌝ , avols[v][vtblpnum3].mapped?, avols[v][vtblpnum3].fill < apebs[n1].fill, vtblpnum5 < apebs[n1].fill, vtblpnum3 < # vols[v], vtblpnum3 < # avols[v], n1 < # wlar, abs(avols, apebs, vols, q), 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 ⊦ VTBL_VOLID ∈ vols

Rule argument

Additional information

Used simplifier rules: lf-elim-unmapped: ⊦ vols[v][m] ≠ unmapped → (∃ n. vols[v][m] = ⌜n⌝ );%lf-mapped-in-apebs: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ valid-ebatbl(apebs, wlar, vols, n0) → n < # apebs;% ⊦ unmapped ≠ ⌜m⌝ ; (s)% ⊦ ⌜m⌝ .pnum = m; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%abs-vols-mapped: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ abs(avols, apebs, vols, q) → avols[v][m].mapped?; (forward) from specification ubi-abs% ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%⊦ v ∈ avols ∧ m < # avols[v] ∧ abs(avols, apebs, vols, q) → m < # vols[v]; (ss)% ⊦ v ∈ avols ∧ abs(avols, apebs, vols, q) → v ∈ vols; (ss)