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Proof step 11 from proof refine-write (previous step)

# apebs = # wlar, vols[v][vtblpnum3] = unmapped, apebs1 = apebs, q1 = q, vols1 = vols, 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, vtblpnum5 + n ≤ LEB_SIZE, n + n0 ≤ # buf, n0 + n ≤ # buf, ¬ avols[v][vtblpnum3].mapped?, ¬ VTBL_VOLID ∈ vols ⊦ [ubi_write_multiple#(v, vtblpnum3, vtblpnum5, n0, n, buf, bflipset, vtblpnum4; vols, wlar, q, sqnum, apebs; err)] ( # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs, q) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum4) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum4) ∧ ubi-io-inv(apebs) ∧ id(apebs, apebs1, mapped-pebs(vols1)) ∧ q.lebrefs ⊆ q1.lebrefs ++ (v × vtblpnum3) ∧ (n = 0 → q.lebrefs ⊆ q1.lebrefs) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err ≠ ESUCCESS → vols = vols1) ∧ ( err = ESUCCESS → (∃ n1. vols = vols1[v, vols1[v][vtblpnum3, ⌜n1⌝ ]] ∧ (n ≠ 0 → apebs[n1].fill = vtblpnum5 + n) ∧ (n = 0 → apebs[n1].fill = 0) ∧ apebs[n1].data = mkempbuf(vtblpnum5) + subarray(buf, n0, n) + mkempbuf(LEB_SIZE - n - vtblpnum5))) → ⟨ebm_write#(v, vtblpnum3, vtblpnum5, n0, n, buf; avols; err0)⟩ (abs(avols, apebs, vols, q) ∧ err = err0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [LEB_SIZE - n, vtblpnum5, n2]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: LEB_SIZE - n, vtblpnum5, n2