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Proof step 147 from proof prepost-erase-worker-helper (previous step)

# 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, valid-ebatbl(apebs[m, mkpeb(aehdr, avhdr, buf, m2, true)], wlar[m, wl-entry(m1, erroneous)], vols, vtblpnum1) ∧ valid-eraseq(wlar[m, wl-entry(m1, erroneous)], q0 + q1) ∧ unique-sqns(apebs[m, mkpeb(aehdr, avhdr, buf, m2, true)])

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 6

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]% ⊦ valid-eraseq(wlar, q0 + eq-entry(m, lref) ' + q1) → ¬ # wlar ≤ m; (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)% ⊦ valid-peb(mkpeb(aehdr, avhdr, buf, m, true)) ↔ false; (s)% ⊦ erroneous ≠ erasing; (s)%stat ≠ erasing ⊦ valid-eraseq(wlar, q0 + eq-entry(m, lref) ' + q1) → ( valid-eraseq(wlar[m, wl-entry(m0, stat)], q0 + q1) ↔ ¬ m ∈ q0 ∧ ¬ m ∈ q1); (ss)% ⊦ valid-eraseq(q0 + eq-entry(m, lref) ' + q1) → ¬ m ∈ q0; (s)% ⊦ valid-eraseq(q0 + eq-entry(m, lref) ' + q1) → ¬ m ∈ q1; (s)% ⊦ used ≠ erasing; (s)% ⊦ used ≠ erroneous; (s)%stat ≠ used, stat0 ≠ used ⊦ wlar[m] = wl-entry(m0, stat) → ( valid-ebatbl(apebs, wlar[m, wl-entry(m1, stat0)], vols, n) ↔ valid-ebatbl(apebs, wlar, vols, n)); (ss)%stat ≠ used ⊦ wlar[m] = wl-entry(m0, stat) → ( valid-ebatbl(apebs[m, apeb], wlar, vols, n) ↔ valid-ebatbl(apebs, wlar, vols, n)); (ss)