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Proof step 245 from proof prepost-atomic-leb-change (previous step)

# apebs0 = # wlar, LEB_SIZE = n2 + n0, LEB_SIZE = n4 + # buf1, apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[n1] = wl-entry(m1, free), align↑(datasize(buf, n0), EB_PAGE_SIZE) = n3 + # buf1, aehdr.valid?, n1 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), is-aligned(# buf1, EB_PAGE_SIZE), ubi-io-inv (apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), buf1 + mkempbuf(n4), # buf1, false)]), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), mkempbuf(LEB_SIZE), 0, false)]), ubi-io-inv(apebs0), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-eraseq(q + eq-entry(n1, none) '), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), n3 + # buf1 ≤ # buf, n3 + # buf1 ≤ LEB_SIZE, n0 ≤ LEB_SIZE, n0 ≤ # buf, # buf1 ≤ # buf, # buf1 ≤ LEB_SIZE, ⌊err0⌋ , v ∈ vols ∧ m0 < # vols[v] ∨ v = VTBL_VOLID ∧ m0 = VTBL_LNUM, datasize(buf1, # buf1) < datasize(buf, n0) ∨ checksum(buf1 + mkempbuf(n3), datasize(buf, n0)) ≠ checksum(buf, datasize(buf, n0)) ⊦ vtblpnum1 = n1, valid-eraseq (apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), buf1 + mkempbuf(n4), # buf1, false)], q + eq-entry(n1, none) '), valid-peb(v, m0, mkpeb(aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), buf1 + mkempbuf(n4), # buf1, false)), vtblpnum1 ∈ q, VTBL_VOLID ∈ vols, ∃ buf0. buf = mkempbuf(n0) + buf0

User applied rule insert rewrite lemma

And obtained the following new goals

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, avidhdr (v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), buf1 + mkempbuf(n4), # buf1, false), n1, apebs0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ valid-peb(apeb) → (valid-peb(v, m, apeb) ↔ v = apeb.vidhdr.vol ∧ m = apeb.vidhdr.leb); (ss)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ avidhdr(v, m, m0, m1, m2).vol = v; (s)% ⊦ avidhdr(v, m, m0, m1, m2).leb = m; (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, avidhdr(v, m, n, n0, n2), buf, n1, boolvar)) ↔ valid-peb (v, m, mkpeb(aehdr, avidhdr(v, m, n, n0, n2), buf, n1, boolvar)); (ss)% ⊦ ¬ valid-peb(mkpeb(aehdr, empty, buf, m, boolvar)); (s) Used terms: q + eq-entry(n1, none) ', mkpeb (aehdr, avidhdr (v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), buf1 + mkempbuf(n4), # buf1, false), n1, apebs0