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Proof step 202 from proof prepost-write-once (previous step)

# apebs2 = # wlar0, # apebs0 = # wlar1, q0.head = eq-entry(m4, lref0), LEB_SIZE = (n1 + m0) + m1, vols0[v][m] = unmapped, wlar0[vtblpnum] = wl-entry(m5, free), apebs2[vtblpnum] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), aehdr.valid?, m < # vols0[v], vtblpnum < # wlar0, bflipset-cons(bflipset, wlar1), bflipset-cons(bflipset, wlar0), id(apebs2, apebs0, mapped-pebs(vols0)), is-aligned(m1, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs2), ubi-io-inv(apebs2[vtblpnum, mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false)]), unique-sqns(apebs0), unique-sqns(apebs2), valid-ebatbl(apebs0, wlar1, vols0, vtblpnum2), valid-ebatbl(apebs2, wlar0, vols0, vtblpnum2), valid-eraseq(apebs2, q1 + eq-entry(vtblpnum, none) '), valid-eraseq(apebs0, q0), valid-eraseq(wlar1, q0), valid-eraseq(q0), valid-eraseq(q1), valid-eraseq(wlar0, q1), valid-eraseq(apebs2, q1), valid-eraseq(q1 + eq-entry(vtblpnum, none) '), valid-global-sqn(apebs2, sqnum + 1), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs2, sqnum), valid-vtbl(apebs0, vols0, wlar1, vtblpnum2), valid-vtbl(apebs2, vols0, wlar0, vtblpnum2), valid-wl(apebs2, wlar0), valid-wl(apebs0, wlar1), v ∈ vols0, m1 ≤ LEB_SIZE, m1 + m2 ≤ # buf, m0 + m1 ≤ LEB_SIZE, q1.lebrefs ⊆ q0.lebrefs, ⌊err0⌋ , apebs0 = apebs2 ∧ wlar1 = wlar0 ∧ q0 = q1 ∨ id○(apebs0, apebs2, vtblpnum) ∧ id○(wlar1, wlar0, vtblpnum) ∧ q0 = eq-entry(vtblpnum, lref0) ' + q1 ⊦ vtblpnum2 = vtblpnum, avhdr.valid?, vtblpnum2 ∈ q0, VTBL_VOLID ∈ vols0, vtblpnum2 ∈ q1, valid-ebatbl(apebs2[vtblpnum, mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false)], wlar0[vtblpnum, wl-entry(m5, erasing)], vols0, vtblpnum2) ∧ unique-sqns(apebs2[vtblpnum, mkpeb(aehdr, avhdr, mkempbuf(LEB_SIZE), 0, false)])

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 6

Additional information

Used simplifier rules: ⊦ 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)% ⊦ ¬ avhdr.valid? → ¬ valid-peb(mkpeb(aehdr, avhdr, buf, m, boolvar)); (s)% ⊦ used ≠ free; (s)% ⊦ used ≠ erasing; (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)