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Proof step 443 from proof prepost-atomic-leb-change (previous step)

# apebs0 = # wlar, LEB_SIZE = n2 + n0, apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[n1] = wl-entry(m1, free), vols[v][m0] = unmapped, aehdr.valid?, m0 < # vols[v], n1 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0, sqnum + 1), valid-peb(mkpeb(aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), v ∈ vols, n0 ≤ LEB_SIZE ⊦ n1 = vtblpnum1, vtblpnum1 ∈ q, VTBL_VOLID ∈ vols, unique-sqns(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]) ∧ valid-wl(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar[n1, wl-entry(m1, used)]) ∧ valid-eraseq(wlar[n1, wl-entry(m1, used)], q) ∧ valid-ebatbl(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar, vols, vtblpnum1)

User applied rule case distinction

And obtained the following new goals

Proof step 444:
# apebs0 = # wlar, LEB_SIZE = n2 + n0, vols[v][m0] = unmapped, wlar[n1] = wl-entry(m1, free), apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), aehdr.valid?, n1 < # wlar, m0 < # vols[v], bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, 0, 0), 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-global-sqn(apebs0, sqnum + 1), valid-global-sqn(apebs0, sqnum), valid-peb(mkpeb(aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), v ∈ vols, n0 ≤ LEB_SIZE ⊦ n1 = vtblpnum1, valid-wl(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar[n1, wl-entry(m1, used)]), VTBL_VOLID ∈ vols, vtblpnum1 ∈ q

Rule argument

pos: right 4

Additional information

Used simplifier rules: ⊦ used ≠ free; (s)%stat ≠ used ⊦ wlar[m] = wl-entry(m0, stat) → ( valid-ebatbl(apebs[m, apeb], wlar, vols, n) ↔ valid-ebatbl(apebs, wlar, vols, n)); (ss)% ⊦ free ≠ erasing; (s)%stat ≠ erasing ⊦ wlar[n] = wl-entry(m0, stat) → ( valid-eraseq(wlar[n, wl-entry(m1, used)], q) ↔ valid-eraseq(wlar, q)); (ss)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%m < # apebs ⊦ unique-sqns(apebs) → ( unique-sqns(apebs[m, apeb]) ↔ ¬ valid-peb(apeb) ∨ ¬ apeb.vidhdr.sqn ∈ valid-sqns(apeb.vidhdr.vol, apeb.vidhdr.leb, apebs) \ (valid-peb(apeb.vidhdr.vol, apeb.vidhdr.leb, apebs[m]) ⊃ {apebs[m].vidhdr.sqn} ;∅ )); (ss)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ avidhdr(v, m, m0, m1, m2).sqn = m0; (s)% ⊦ avidhdr(v, m, m0, m1, m2).vol = v; (s)% ⊦ avidhdr(v, m, m0, m1, m2).leb = m; (s)% ⊦ ¬ valid-peb(v, m, mkpeb(aehdr, empty, buf, m0, boolvar)); (s)% ⊦ bag \ ∅ = bag; (s)% ⊦ valid-global-sqn(apebs, n) → ¬ n ∈ valid-sqns(v, m, apebs); (s)