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Proof step 3 from proof prepost-write-multiple (previous step)

# apebs0 = # wlar, vols0[v][m] = unmapped, apebs = apebs0, q = q0, vols = vols0, m < # vols0[v], bflipset-cons(bflipset, wlar), is-aligned(m1, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), ubi-io-inv(apebs0), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols0, vtblpnum), valid-eraseq(apebs0, q0), valid-eraseq(wlar, q0), valid-eraseq(q0), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols0, wlar, vtblpnum), valid-wl(apebs0, wlar), v ∈ vols0, m0 + m1 ≤ LEB_SIZE, m1 + m2 ≤ # buf, ¬ vtblpnum ∈ q0, ¬ VTBL_VOLID ∈ vols0 ⊦ ⟪ubi_write_multiple#(v, m, m0, m2, m1, buf, bflipset, vtblpnum; 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, vtblpnum) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum) ∧ ubi-io-inv(apebs) ∧ id(apebs, apebs0, mapped-pebs(vols0)) ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × m) ∧ (m1 = 0 → q.lebrefs ⊆ q0.lebrefs) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err ≠ ESUCCESS → vols = vols0) ∧ ( err = ESUCCESS → (∃ n. vols = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ (m1 ≠ 0 → apebs[n].fill = m0 + m1) ∧ (m1 = 0 → apebs[n].fill = 0) ∧ apebs[n].data = mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(LEB_SIZE - m1 - m0))))

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 - m1, m0, 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 - m1, m0, n2