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Proof step 17 from proof prepost-io-write-data (previous step)

# apebs = # wlar, apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false), wlar[n] = wl-entry(m3, used), err0 = ESUCCESS, aehdr.valid?, avhdr.valid?, n < # apebs, n < # wlar, bflipset-cons(bflipset, wlar), is-aligned(m2, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), ubi-io-inv (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) ]), 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(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, n2), valid-peb(mkpeb(aehdr, avhdr, buf0, m, false)), valid-vtbl(apebs, vols, wlar, n3), valid-wl(apebs, wlar), 0 + m0 ≤ # apebs[n].data, m ≤ m0, m1 + m2 ≤ # buf, m0 + m2 ≤ LEB_SIZE, LEB_SIZE - m0 ≥ m2, LEB_SIZE ≥ m0, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ n3 = n, n3 ∈ q, VTBL_VOLID ∈ vols, n ∈ q, # 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) ] = # wlar ∧ unique-sqns (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) ]) ∧ valid-global-sqn (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) ], n2) ∧ valid-wl (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) ], wlar) ∧ valid-eraseq (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) ], q) ∧ valid-ebatbl (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) ], wlar, vols, n3) ∧ valid-vtbl (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) ], vols, wlar, n3)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# apebs = # wlar, apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false), wlar[n] = wl-entry(m3, used), aehdr.valid?, avhdr.valid?, n < # wlar, bflipset-cons(bflipset, wlar), is-aligned(m2, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-inv(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(LEB_SIZE - m0 - m2), m0 + m2, false)]), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf0, m, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, n3), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, n2), valid-peb(mkpeb(aehdr, avhdr, buf0, m, false)), valid-vtbl(apebs, vols, wlar, n3), valid-wl(apebs, wlar), m ≤ LEB_SIZE, m ≤ m0, m1 + m2 ≤ # buf, m0 + m2 ≤ LEB_SIZE, m2 + m0 ≤ LEB_SIZE, m0 ≤ LEB_SIZE ⊦ n3 = n, n3 ∈ q, VTBL_VOLID ∈ vols, n ∈ q, unique-sqns(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(LEB_SIZE - m0 - m2), m0 + m2, false)]) ∧ valid-global-sqn(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(LEB_SIZE - m0 - m2), m0 + m2, false)], n2) ∧ valid-wl(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(LEB_SIZE - m0 - m2), m0 + m2, false)], wlar) ∧ valid-eraseq(apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(LEB_SIZE - m0 - m2), m0 + m2, false)], q) ∧ valid-ebatbl (apebs[n, mkpeb(aehdr, avhdr, subarray(buf0, 0, m0) + subarray(buf, m1, m2) + mkempbuf(LEB_SIZE - m0 - m2), m0 + m2, false)], wlar, vols, n3)

Rule argument

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)%⊦ ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, n, boolvar)) → # buf = LEB_SIZE; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%⊦ m ≠ n0 → ( valid-vtbl(apebs[m, apeb], vols, wlar, n0) ↔ valid-vtbl(apebs, vols, wlar, n0)); (s)% ⊦ # apebs[n, apeb] = # apebs; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (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)%n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ n ≥ m ↔ m ≤ n; (s)