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Proof step 468 from proof prepost-atomic-leb-change (previous step)

# apebs0 = # wlar, LEB_SIZE = n2 + n0, wlar[n1] = wl-entry(m1, free), apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), aehdr.valid?, n1 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false)]), ubi-io-inv(apebs0), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(apebs0, q + eq-entry(n1, none) '), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-eraseq(q + eq-entry(n1, none) '), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), n0 ≤ LEB_SIZE, ⌊err0⌋ , v ∈ vols ∧ m0 < # vols[v] ∨ v = VTBL_VOLID ∧ m0 = VTBL_LNUM ⊦ vtblpnum1 = n1, avhdr.valid?, vtblpnum1 ∈ q, VTBL_VOLID ∈ vols, valid-ebatbl(apebs0[n1, mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false)], wlar[n1, wl-entry(m1, erasing)], vols, vtblpnum1) ∧ valid-wl(apebs0[n1, mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false)], wlar[n1, wl-entry(m1, erasing)]) ∧ valid-global-sqn(apebs0[n1, mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false)], sqnum + 1) ∧ unique-sqns(apebs0[n1, mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 469:
m < # apebs ⊦ ¬ valid-peb(apeb) ∧ valid-global-sqn(apebs, n) → valid-global-sqn(apebs[m, apeb], n)
Proof step 470:
# apebs0 = # wlar, LEB_SIZE = n2 + n0, apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[n1] = wl-entry(m1, free), aehdr.valid?, n1 < # wlar, n1 < # apebs0, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false)]), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(q + eq-entry(n1, none) '), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-eraseq(apebs0, q + eq-entry(n1, none) '), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0, sqnum + 1), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), n0 ≤ LEB_SIZE, ⌊err0⌋ , v ∈ vols ∧ m0 < # vols[v] ∨ v = VTBL_VOLID ∧ m0 = VTBL_LNUM ⊦ vtblpnum1 = n1, avhdr.valid?, valid-peb(mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false)), VTBL_VOLID ∈ vols, vtblpnum1 ∈ q, valid-ebatbl(apebs0[n1, mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false)], wlar[n1, wl-entry(m1, erasing)], vols, vtblpnum1) ∧ valid-wl(apebs0[n1, mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false)], wlar[n1, wl-entry(m1, erasing)]) ∧ true ∧ unique-sqns(apebs0[n1, mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false)])

Rule argument

spec: ubi-base name: valid-global-sqn-invalidate seq: m < # apebs ⊦ ¬ valid-peb(apeb) ∧ valid-global-sqn(apebs, n) → valid-global-sqn(apebs[m, apeb], n) subst: [n, apeb, m, apebs] → [sqnum + 1, mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false), n1, apebs0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ avhdr.valid? → ¬ valid-peb(mkpeb(aehdr, avhdr, buf, m, boolvar)); (s)% ⊦ valid-global-sqn(apebs, n) → valid-global-sqn(apebs, n + m); (ss)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ ¬ n < n; (s) Used terms: sqnum + 1, mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false), n1, apebs0