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Proof step 321 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), aehdr.valid?, vtblpnum1 < # wlar, n1 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, 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-eraseq(q + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) '), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), n0 ≤ LEB_SIZE ⊦ vtblpnum1 = n1, VTBL_VOLID ∈ vols, vtblpnum1 ∈ q, ( ¬ v ∈ vols ∧ is-encoded(to-vtbl(vols)[v, m], mkempbuf(LEB_SIZE)) ∧ n0 = LEB_SIZE → valid-ebatbl (apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar[vtblpnum1, wl-entry(wlar[vtblpnum1].ec, erasing)][n1, wl-entry(m1, used)], vols[v, fill(mkebatbl(m), unmapped)], n1) ∧ valid-vtbl (apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], vols[v, fill(mkebatbl(m), unmapped)], wlar[vtblpnum1, wl-entry(wlar[vtblpnum1].ec, erasing)][n1, wl-entry(m1, used)], n1)) ∧ ( is-encoded(to-vtbl(vols), mkempbuf(LEB_SIZE)) ∧ n0 = LEB_SIZE → valid-ebatbl (apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar[vtblpnum1, wl-entry(wlar[vtblpnum1].ec, erasing)][n1, wl-entry(m1, used)], vols, n1) ∧ valid-vtbl (apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], vols, wlar[vtblpnum1, wl-entry(wlar[vtblpnum1].ec, erasing)][n1, wl-entry(m1, used)], n1)) ∧ bflipset-cons(bflipset -- vtblpnum1, wlar[vtblpnum1, wl-entry(wlar[vtblpnum1].ec, erasing)][n1, wl-entry(m1, used)]) ∧ valid-eraseq (apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], q + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ valid-eraseq(wlar[vtblpnum1, wl-entry(wlar[vtblpnum1].ec, erasing)][n1, wl-entry(m1, used)], q + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ valid-wl (apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar[vtblpnum1, wl-entry(wlar[vtblpnum1].ec, erasing)][n1, wl-entry(m1, used)]) ∧ valid-global-sqn(apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], sqnum + 1) ∧ unique-sqns(apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 322:
# apebs0 = # wlar, LEB_SIZE = n2 + n0, wlar[n1] = wl-entry(m1, free), apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[vtblpnum1] = wl-entry(m0, stat), aehdr.valid?, n1 < # wlar, vtblpnum1 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]), ubi-io-inv(apebs0), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(q + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) '), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), n0 ≤ LEB_SIZE ⊦ vtblpnum1 = n1, vtblpnum1 ∈ q, VTBL_VOLID ∈ vols, ( ¬ v ∈ vols ∧ is-encoded(to-vtbl(vols)[v, m], mkempbuf(LEB_SIZE)) ∧ n0 = LEB_SIZE → valid-ebatbl (apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar[vtblpnum1, wl-entry(m0, erasing)][n1, wl-entry(m1, used)], vols[v, fill(mkebatbl(m), unmapped)], n1) ∧ valid-vtbl (apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], vols[v, fill(mkebatbl(m), unmapped)], wlar[vtblpnum1, wl-entry(m0, erasing)][n1, wl-entry(m1, used)], n1)) ∧ ( is-encoded(to-vtbl(vols), mkempbuf(LEB_SIZE)) ∧ n0 = LEB_SIZE → valid-ebatbl (apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar[vtblpnum1, wl-entry(m0, erasing)][n1, wl-entry(m1, used)], vols, n1) ∧ valid-vtbl (apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], vols, wlar[vtblpnum1, wl-entry(m0, erasing)][n1, wl-entry(m1, used)], n1)) ∧ bflipset-cons(bflipset -- vtblpnum1, wlar[vtblpnum1, wl-entry(m0, erasing)][n1, wl-entry(m1, used)]) ∧ valid-eraseq (apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], q + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ valid-eraseq(wlar[vtblpnum1, wl-entry(m0, erasing)][n1, wl-entry(m1, used)], q + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ valid-wl (apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], wlar[vtblpnum1, wl-entry(m0, erasing)][n1, wl-entry(m1, used)]) ∧ valid-global-sqn(apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)], sqnum + 1) ∧ unique-sqns(apebs0[n1, mkpeb(aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)])

Rule argument

spec: wlentry name: elim-02 seq: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat) subst: [wle, m, stat] → [wlar[vtblpnum1], m0, stat]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar[vtblpnum1], m0, stat