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Proof step 7 from proof refine-write (previous step)

# apebs = # wlar, buf0 = buf, ebae = unmapped, ebae = vols[v][vtblpnum2], vtblpnum = vtblpnum4, vtblpnum0 = EB_PAGE_SIZE, vtblpnum1 = vtblpnum5, vtblpnum2 = vtblpnum3, vtblpnum2 < # vols[v], vtblpnum3 < # avols[v], abs(avols, apebs, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(vtblpnum1, EB_PAGE_SIZE), 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 ∈ vols, v ∈ avols, vtblpnum1 + n ≤ LEB_SIZE, n0 + n ≤ # buf0, n + n0 ≤ # buf, vtblpnum5 + n ≤ LEB_SIZE, vols[v][vtblpnum2] ≠ unmapped → apebs[vols[v][vtblpnum2].pnum].fill ≤ vtblpnum1, 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)), avols[v][vtblpnum3].mapped? → avols[v][vtblpnum3].fill ≤ vtblpnum5 ⊦ ⟪ubi_write_multiple#(v, vtblpnum2, vtblpnum1, n0, n, buf0, bflipset, vtblpnum; vols, wlar, q, sqnum, apebs; err)⟫ ⟨ebm_write#(v, vtblpnum3, vtblpnum5, n0, n, buf; avols; err0)⟩ (abs(avols, apebs, vols, q) ∧ err = err0), VTBL_VOLID ∈ vols

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
# apebs = # wlar, vols[v][vtblpnum3] = unmapped, vtblpnum3 < # vols[v], vtblpnum3 < # avols[v], 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 ∈ vols, v ∈ avols, n0 + n ≤ # buf, n + n0 ≤ # buf, vtblpnum5 + n ≤ LEB_SIZE, ¬ avols[v][vtblpnum3].mapped?, ¬ VTBL_VOLID ∈ vols ⊦ ⟪ubi_write_multiple#(v, vtblpnum3, vtblpnum5, n0, n, buf, bflipset, vtblpnum4; vols, wlar, q, sqnum, apebs; err)⟫ ⟨ebm_write#(v, vtblpnum3, vtblpnum5, n0, n, buf; avols; err0)⟩ (abs(avols, apebs, vols, q) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%abs-vols-unmapped: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = unmapped ∧ abs(avols, apebs, vols, q) → ¬ avols[v][m].mapped?; (forward) from specification ubi-abs%f: ⊦ m < n → n ≠ 0; (forward) 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)