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Proof step 152 from proof prepost-atomic-leb-change (previous step)

# apebs0 = # wlar, LEB_SIZE = n4 + align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), LEB_SIZE = n2 + n0, LEB_SIZE = n3 + align↑(datasize(buf, n0), EB_PAGE_SIZE), apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[n1] = wl-entry(m1, free), vols[v][m0] = ⌜m⌝ , wlar[m] = wl-entry(m2, used), aehdr.valid?, m < # wlar, m0 < # vols[v], n1 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), 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), ubi-io-inv (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ]), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(q + eq-entry(m, v × m0) '), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-peb(v, m0, apebs0[m]), valid-peb (mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, n0) + mkempbuf(n2), align↑(datasize(buf, n0), EB_PAGE_SIZE), false)), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), v ∈ vols, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE) ≤ LEB_SIZE, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ # buf, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ LEB_SIZE, n0 ≤ LEB_SIZE, n0 ≤ # buf ⊦ m = vtblpnum1, vtblpnum1 = n1, bflipset-cons(bflipset -- m, wlar[m, wl-entry(m2, erasing)][n1, wl-entry(m1, used)]), VTBL_VOLID ∈ vols, vtblpnum1 ∈ q, m ∈ q, ∃ buf0. buf = mkempbuf(n0) + buf0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-base name: bitflip-cons-set-used seq: ⊦ bflipset-cons(bflipset, wlar) → bflipset-cons(bflipset, wlar[m, wl-entry(n, used)]) subst: [n, m, wlar, bflipset] → [m1, n1, wlar[m, wl-entry(m2, erasing)], bflipset -- m] flags: <all paths>

Additional information

Used simplifier rules: ⊦ wl-entry(m, stat).status = stat; (s)% ⊦ used ≠ erasing; (s)%wle.status ≠ used ⊦ bflipset-cons(bflipset, wlar[m, wle]) ↔ bflipset-cons(bflipset, wlar) ∧ ¬ m ∈ bflipset; (s)% ⊦ bflipset-cons(bflipset, wlar) → bflipset-cons(bflipset -- n, wlar); (ss)% ⊦ n ∈ ns -- n0 ↔ n ≠ n0 ∧ n ∈ ns; (s) Used terms: m1, n1, wlar[m, wl-entry(m2, erasing)], bflipset -- m