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Proof step 465 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(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-eraseq(apebs0[n1, mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false)], q + eq-entry(n1, none) ') ∧ 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 466:
m < # apebs ⊦ ¬ valid-peb(apeb) ∧ valid-eraseq(apebs, q) → valid-eraseq(apebs[m, apeb], q)
Proof step 467:
# 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-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) ∧ true ∧ 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)])

Rule argument

spec: ubi-base name: valid-eraseqp-invalidate seq: m < # apebs ⊦ ¬ valid-peb(apeb) ∧ valid-eraseq(apebs, q) → valid-eraseq(apebs[m, apeb], q) subst: [q, apeb, m, apebs] → [q + eq-entry(n1, none) ', 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-eraseq(apebs, q) → ( valid-eraseq(apebs, q + eq-entry(n, lref) ') ↔ n < # apebs ∧ ( valid-peb(apebs[n]) → lref = apebs[n].vidhdr.vol × apebs[n].vidhdr.leb)); (ss)% ⊦ none ≠ v × m; (s)%a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]% ⊦ ¬ valid-peb(mkpeb(aehdr, empty, buf, m, boolvar)); (s) Used terms: q + eq-entry(n1, none) ', mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false), n1, apebs0