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Proof step 423 from proof prepost-atomic-leb-change (previous step)

# apebs0 = # wlar, LEB_SIZE = n2 + n0, wlar[m] = wl-entry(m2, used), vols[v][m0] = ⌜m⌝ , wlar[n1] = wl-entry(m1, free), apebs0[n1] = mkpeb(aechdr(m3), empty, mkempbuf(LEB_SIZE), 0, false), m0 < # vols[v], n1 < # wlar, m < # wlar, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset -- m, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0[n1, mkpeb(aechdr(m3), avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]), ubi-io-inv(apebs0), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-eraseq(q + eq-entry(m, v × m0) '), valid-global-sqn(apebs0, sqnum + 1), valid-peb(mkpeb(aechdr(m3), avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)), valid-peb(v, m0, apebs0[m]), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), v ∈ vols, sqnum ≤ valid-sqns(v, m0, apebs0).max, n0 ≤ LEB_SIZE, ∀ v0, m4. valid-sqns(v0, m4, apebs0) ≠ ∅ → valid-sqns(v0, m4, apebs0).max < sqnum ⊦ m = vtblpnum1, vtblpnum1 = n1, valid-wl (apebs0[n1, mkpeb(aechdr(m3), avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar[m, wl-entry(m2, erasing)][n1, wl-entry(m1, used)]), m ∈ q, vtblpnum1 ∈ q, VTBL_VOLID ∈ vols

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 29 terms: v, m0

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # apebs ⊦ valid-peb(v, m, apebs[n]) → valid-sqns(v, m, apebs) ≠ ∅; (s)% ⊦ m ≤ n → (n < m ↔ false); (s) Used terms: v, m0