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Proof step 59 from proof inv-write (previous step)

# apebs0 = # wlar, # apebs1 = # wlar, wlar[m0] = wl-entry(m1, used), apebs1[m0] = mkpeb(aehdr, avhdr, buf2, m, false), vols[v][vtblpnum4] = ⌜m0⌝ , apebs0[m0] = mkpeb(aehdr0, avhdr0, buf3, m2, false), buf0 = mkbuf(vtblpnum3 + n2), err = err0, n = vtblpnum3, n0 = 0, m0 < # wlar, vtblpnum4 < # vols[v], bflipset-cons(bflipset, wlar), is-aligned(vtblpnum3, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs1), ubi-io-peb-inv(mkpeb(aehdr0, avhdr0, buf3, m2, false)), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m, false)), unique-sqns(apebs0), unique-sqns(apebs1), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-ebatbl(apebs1, wlar, vols, vtblpnum1), valid-eraseq(apebs0, q), valid-eraseq(apebs1, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs1, sqnum), valid-peb(mkpeb(aehdr0, avhdr0, buf3, m2, false)), valid-peb(mkpeb(aehdr, avhdr, buf2, m, false)), valid-peb(v, vtblpnum4, mkpeb(aehdr, avhdr, buf2, m, false)), valid-peb(v, vtblpnum4, mkpeb(aehdr0, avhdr0, buf3, m2, false)), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-vtbl(apebs1, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), valid-wl(apebs1, wlar), v ∈ vols, m ≤ LEB_SIZE, vtblpnum3 ≤ LEB_SIZE, vtblpnum3 + n2 ≤ LEB_SIZE, n1 + n2 ≤ # buf, m ≤ vtblpnum3, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ err = ESUCCESS, err1 = ESUCCESS, m0 = vtblpnum1, n2 = 0, vtblpnum1 ∈ q, m0 ∈ q, VTBL_VOLID ∈ vols, ∀ buf. # buf = # buf0 → range=(buf, 0, buf0, 0, n0) → # buf0 ≥ n0 + n

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ m + n < m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ n ≥ m ↔ m ≤ n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ 0 ≤ m; (s)% ⊦ range=(buf, n0, buf0, n1, 0) ↔ n0 ≤ # buf ∧ n1 ≤ # buf0; (s)% ⊦ # mkbuf(n) = n; (s)