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Proof step 11 from proof prepost-io-write-data (previous step)

# apebs = # wlar, wlar[n] = wl-entry(m3, used), apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false), n0 = m2, n1 = m1, vtblpnum = m0, vtblpnum0 = n, avhdr.valid?, aehdr.valid?, n < # wlar, bflipset-cons(bflipset, wlar), is-aligned(m0, EB_PAGE_SIZE), is-aligned(m2, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf0, m, false)), ubi-io-write-data-pre(vtblpnum0, vtblpnum, n1, n0, buf, apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, n3), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, n2), valid-peb(mkpeb(aehdr, avhdr, buf0, m, false)), valid-vtbl(apebs, vols, wlar, n3), valid-wl(apebs, wlar), m0 + m2 ≤ LEB_SIZE, m1 + m2 ≤ # buf, m ≤ m0 ⊦ [fail_or_success#(; ; err); if err = ESUCCESS then apebs[vtblpnum0] := mkpeb (apebs[vtblpnum0].echdr, apebs[vtblpnum0].vidhdr, subarray(apebs[vtblpnum0].data, 0, vtblpnum) + subarray(buf, n1, n0) + mkempbuf(LEB_SIZE - vtblpnum - n0), vtblpnum + n0, apebs[vtblpnum0].bad) else choose n with (n < n0 ∨ n = 0 ∧ n0 = 0) ∧ is-aligned(n, EB_PAGE_SIZE) in if n ≠ 0 then apebs[vtblpnum0] := mkpeb (apebs[vtblpnum0].echdr, apebs[vtblpnum0].vidhdr, subarray(apebs[vtblpnum0].data, 0, vtblpnum) + subarray(buf, n1, n) + mkempbuf(LEB_SIZE - vtblpnum - n), vtblpnum + n, apebs[vtblpnum0].bad)] ( ubi-io-inv(apebs) → # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, n2) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(apebs, q) ∧ valid-ebatbl(apebs, wlar, vols, n3) ∧ valid-vtbl(apebs, vols, wlar, n3)), n3 = n, n3 ∈ q, VTBL_VOLID ∈ vols, n ∈ q

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# apebs = # wlar, wlar[n] = wl-entry(m3, used), apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false), n3 ≠ n, avhdr.valid?, aehdr.valid?, n < # wlar, bflipset-cons(bflipset, wlar), is-aligned(m0, EB_PAGE_SIZE), is-aligned(m2, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf0, m, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, n3), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, n2), valid-peb(mkpeb(aehdr, avhdr, buf0, m, false)), valid-vtbl(apebs, vols, wlar, n3), valid-wl(apebs, wlar), m0 + m2 ≤ LEB_SIZE, m1 + m2 ≤ # buf, m ≤ m0, ¬ n3 ∈ q, ¬ VTBL_VOLID ∈ vols, ¬ n ∈ q ⊦ [fail_or_success#(; ; err); if err = ESUCCESS then apebs[n] := mkpeb (apebs[n].echdr, apebs[n].vidhdr, subarray(apebs[n].data, 0, m0) + subarray(buf, m1, m2) + mkempbuf(LEB_SIZE - m0 - m2), m0 + m2, apebs[n].bad) else choose n2 with (n2 < m2 ∨ n2 = 0 ∧ m2 = 0) ∧ is-aligned(n2, EB_PAGE_SIZE) in if n2 ≠ 0 then apebs[n] := mkpeb (apebs[n].echdr, apebs[n].vidhdr, subarray(apebs[n].data, 0, m0) + subarray(buf, m1, n2) + mkempbuf(LEB_SIZE - m0 - n2), m0 + n2, apebs[n].bad)] ( ubi-io-inv(apebs) → # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, n2) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(apebs, q) ∧ valid-ebatbl(apebs, wlar, vols, n3) ∧ valid-vtbl(apebs, vols, wlar, n3))

Rule argument

Additional information

Used simplifier rules: lf-vtbl-info: ⊦ valid-vtbl(apebs, vols, wlar, n) ∧ valid-eraseq(wlar, q) → ¬ n ∈ q;% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).fill = m; (s)%⊦ ubi-io-write-data-pre(n, n0, n1, n2, buf, apebs) ↔ n < # apebs ∧ ¬ apebs[n].bad ∧ apebs[n].echdr.valid? ∧ apebs[n].vidhdr.valid? ∧ is-aligned(n0, EB_PAGE_SIZE) ∧ is-aligned(n2, EB_PAGE_SIZE) ∧ apebs[n].fill ≤ n0 ∧ n0 + n2 ≤ LEB_SIZE ∧ n1 + n2 ≤ # buf; (s)