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Proof step 84 from proof prepost-write-once (previous step)

# apebs2 = # wlar0, # apebs0 = # wlar, q0.head = eq-entry(m4, lref), LEB_SIZE = (n0 + m1) + m0, apebs2[vtblpnum1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar0[vtblpnum1] = wl-entry(m5, free), vols0[v][m] = unmapped, aehdr.valid?, vtblpnum1 < # wlar0, m < # vols0[v], bflipset-cons(bflipset, wlar0), bflipset-cons(bflipset, wlar), id(apebs2, apebs0, mapped-pebs(vols0)), is-aligned(m0, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), ubi-io-inv(apebs2), ubi-io-inv(apebs0), ubi-io-inv(apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(LEB_SIZE), 0, false)]), ubi-io-inv(apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), m0 + m1, false)]), unique-sqns(apebs2), unique-sqns(apebs0), valid-ebatbl(apebs2, wlar0, vols0, vtblpnum2), valid-ebatbl(apebs0, wlar, vols0, vtblpnum2), valid-eraseq(apebs2, q1), valid-eraseq(wlar0, q1), valid-eraseq(q1), valid-eraseq(q0), valid-eraseq(wlar, q0), valid-eraseq(apebs0, q0), valid-global-sqn(apebs2, sqnum), valid-global-sqn(apebs0, sqnum), valid-peb(mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), m0 + m1, false)), valid-vtbl(apebs2, vols0, wlar0, vtblpnum2), valid-vtbl(apebs0, vols0, wlar, vtblpnum2), valid-wl(apebs2, wlar0), valid-wl(apebs0, wlar), v ∈ vols0, m0 + m1 ≤ LEB_SIZE, m1 + m2 ≤ # buf, m1 ≤ LEB_SIZE, m2 + m1 ≤ # buf, m0 ≤ LEB_SIZE, m1 + m0 ≤ LEB_SIZE, q1.lebrefs ⊆ q0.lebrefs, apebs0 = apebs2 ∧ wlar = wlar0 ∧ q0 = q1 ∨ id○(apebs0, apebs2, vtblpnum1) ∧ id○(wlar, wlar0, vtblpnum1) ∧ q0 = eq-entry(vtblpnum1, lref) ' + q1 ⊦ m1 = 0, vtblpnum2 = vtblpnum1, vtblpnum2 ∈ q1, VTBL_VOLID ∈ vols0, vtblpnum2 ∈ q0, ∃ n. vols0[v, vols0[v][m, ⌜vtblpnum1⌝ ]] = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), m0 + m1, false)][n].fill = m0 + m1 ∧ apebs2[vtblpnum1, mkpeb(aehdr, avidhdr(v, m, sqnum, 0, 0), mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0), m0 + m1, false)][n].data = mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n0)

User applied rule exists right

And closed the goal!

Rule argument

pos: right 6 terms: vtblpnum1 abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%m < # apebs ⊦ apebs[m, apeb][m] = apeb; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).fill = m; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)% ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer] Used terms: vtblpnum1