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Proof step 141 from proof prepost-erase-worker-helper (previous step)

# apebs0 = # wlar0, # apebs = # wlar0, # wlar = # wlar0, wlar[m] = wl-entry(m1, erasing), wlar0[m] = wl-entry(m0, erasing), apebs[m] = mkpeb(aehdr, avhdr, buf, m2, false), m < # wlar0, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar0), id○(apebs, apebs0, m), id○(wlar, wlar0, m), ubi-io-inv(apebs), ubi-io-inv(apebs0), ubi-io-inv(apebs[m, mkpeb(aehdr, avhdr, buf, m2, true)]), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, m2, false)), unique-sqns(apebs), unique-sqns(apebs0), valid-ebatbl(apebs, wlar, vols, vtblpnum1), valid-ebatbl(apebs0, wlar0, vols, vtblpnum1), valid-eraseq(wlar, q0 + eq-entry(m, lref) ' + q1), valid-eraseq(apebs, q0 + eq-entry(m, lref) ' + q1), valid-eraseq(q0 + eq-entry(m, lref) ' + q1), valid-eraseq(wlar0, q0 + eq-entry(m, lref) ' + q1), valid-eraseq(apebs0, q0 + eq-entry(m, lref) ' + q1), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum1), valid-vtbl(apebs0, vols, wlar0, vtblpnum1), valid-wl(apebs, wlar), valid-wl(apebs0, wlar0) ⊦ err1 = ESUCCESS, vtblpnum1 = m, VTBL_VOLID ∈ vols, vtblpnum1 ∈ q0, vtblpnum1 ∈ q1, valid-ebatbl(apebs[m, mkpeb(aehdr, avhdr, buf, m2, true)], wlar[m, wl-entry(m1, erroneous)], vols, vtblpnum1) ∧ valid-eraseq(apebs[m, mkpeb(aehdr, avhdr, buf, m2, true)], q0 + q1) ∧ valid-eraseq(wlar[m, wl-entry(m1, erroneous)], q0 + q1) ∧ valid-wl(apebs[m, mkpeb(aehdr, avhdr, buf, m2, true)], wlar[m, wl-entry(m1, erroneous)]) ∧ unique-sqns(apebs[m, mkpeb(aehdr, avhdr, buf, m2, true)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 142:
⊦ ¬ m ∈ q → (valid-eraseq(apebs[m, apeb], q) ↔ valid-eraseq(apebs, q))
Proof step 143:
# wlar = # wlar0, # apebs = # wlar0, # apebs0 = # wlar0, apebs[m] = mkpeb(aehdr, avhdr, buf, m2, false), wlar0[m] = wl-entry(m0, erasing), wlar[m] = wl-entry(m1, erasing), m < # wlar0, bflipset-cons(bflipset, wlar0), bflipset-cons(bflipset, wlar), id○(wlar, wlar0, m), id○(apebs, apebs0, m), ubi-io-inv(apebs[m, mkpeb(aehdr, avhdr, buf, m2, true)]), ubi-io-inv(apebs0), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, m2, false)), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs0, wlar0, vols, vtblpnum1), valid-ebatbl(apebs, wlar, vols, vtblpnum1), valid-eraseq(apebs0, q0 + eq-entry(m, lref) ' + q1), valid-eraseq(wlar0, q0 + eq-entry(m, lref) ' + q1), valid-eraseq(q0 + eq-entry(m, lref) ' + q1), valid-eraseq(apebs, q0 + eq-entry(m, lref) ' + q1), valid-eraseq(wlar, q0 + eq-entry(m, lref) ' + q1), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs0, vols, wlar0, vtblpnum1), valid-vtbl(apebs, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar0), valid-wl(apebs, wlar) ⊦ err1 = ESUCCESS, vtblpnum1 = m, vtblpnum1 ∈ q1, vtblpnum1 ∈ q0, VTBL_VOLID ∈ vols, m ∈ q0 + q1, valid-ebatbl(apebs[m, mkpeb(aehdr, avhdr, buf, m2, true)], wlar[m, wl-entry(m1, erroneous)], vols, vtblpnum1) ∧ valid-eraseq(apebs, q0 + q1) ∧ valid-eraseq(wlar[m, wl-entry(m1, erroneous)], q0 + q1) ∧ valid-wl(apebs[m, mkpeb(aehdr, avhdr, buf, m2, true)], wlar[m, wl-entry(m1, erroneous)]) ∧ unique-sqns(apebs[m, mkpeb(aehdr, avhdr, buf, m2, true)])

Rule argument

spec: ubi-base name: valid-eraseqp-update-other seq: ⊦ ¬ m ∈ q → (valid-eraseq(apebs[m, apeb], q) ↔ valid-eraseq(apebs, q)) subst: [q, apeb, m, apebs] → [q0 + q1, mkpeb(aehdr, avhdr, buf, m2, true), m, apebs] flags: <all paths>

Additional information

Used simplifier rules: a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]% ⊦ valid-eraseq(q0 + eq-entry(m, lref) ' + q1) → ¬ m ∈ q0 + q1; (s) Used terms: q0 + q1, mkpeb(aehdr, avhdr, buf, m2, true), m, apebs