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Proof step 3 from proof inv-change (previous step)

# apebs = # wlar, apebs0 = apebs, q0 = q, vols0 = vols, vtblpnum1 < # vols[v], bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-wl(apebs, wlar), v ∈ vols, n0 ≤ # buf, n0 ≤ LEB_SIZE, ¬ vtblpnum ∈ q, ¬ VTBL_VOLID ∈ vols ⊦ ⟪ubi_change#(v, vtblpnum1, n0, buf, EB_PAGE_SIZE; vols, wlar, q, bflipset, vtblpnum, 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) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err ≠ ESUCCESS → vols = vols0 ∧ id(apebs, apebs0, mapped-pebs(vols0)) ∧ q.lebrefs ⊆ q0.lebrefs) ∧ ( err = ESUCCESS → v ∈ vols0 ∧ vtblpnum1 < # vols0[v] ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × vtblpnum1) ∧ (vols0[v][vtblpnum1] ≠ unmapped → id(apebs, apebs0, mapped-pebs(vols0) -- vols0[v][vtblpnum1].pnum)) ∧ (vols0[v][vtblpnum1] = unmapped → id(apebs, apebs0, mapped-pebs(vols0))) ∧ (∃ n. vols = vols0[v, vols0[v][vtblpnum1, ⌜n⌝ ]] ∧ apebs[n].data = subarray(buf, 0, n0) + mkempbuf(LEB_SIZE - n0) ∧ apebs[n].fill = align↑(datasize(buf, n0), EB_PAGE_SIZE))))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
# apebs = # wlar, LEB_SIZE = n1 + n0, apebs0 = apebs, q0 = q, vols0 = vols, vtblpnum1 < # vols[v], bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-wl(apebs, wlar), v ∈ vols, n0 ≤ LEB_SIZE, n0 ≤ # buf ⊦ ⟪ubi_change#(v, vtblpnum1, n0, buf, EB_PAGE_SIZE; vols, wlar, q, bflipset, vtblpnum, 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) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err ≠ ESUCCESS → vols = vols0 ∧ id(apebs, apebs0, mapped-pebs(vols0)) ∧ q.lebrefs ⊆ q0.lebrefs) ∧ ( err = ESUCCESS → v ∈ vols0 ∧ vtblpnum1 < # vols0[v] ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × vtblpnum1) ∧ (vols0[v][vtblpnum1] ≠ unmapped → id(apebs, apebs0, mapped-pebs(vols0) -- vols0[v][vtblpnum1].pnum)) ∧ (vols0[v][vtblpnum1] = unmapped → id(apebs, apebs0, mapped-pebs(vols0))) ∧ (∃ n. vols = vols0[v, vols0[v][vtblpnum1, ⌜n⌝ ]] ∧ apebs[n].data = subarray(buf, 0, n0) + mkempbuf(n1) ∧ apebs[n].fill = align↑(datasize(buf, n0), EB_PAGE_SIZE)))), vtblpnum ∈ q, VTBL_VOLID ∈ vols

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [n0, LEB_SIZE, n1]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n0, LEB_SIZE, n1