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Proof step 58 from proof inv-write (previous step)

# apebs1 = # wlar, # apebs0 = # wlar, apebs0[m0] = mkpeb(aehdr0, avhdr0, buf3, m2, false), vols[v][vtblpnum4] = ⌜m0⌝ , apebs1[m0] = mkpeb(aehdr, avhdr, buf2, m, false), wlar[m0] = wl-entry(m1, used), vtblpnum4 < # vols[v], m0 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n2, EB_PAGE_SIZE), is-aligned(vtblpnum3, EB_PAGE_SIZE), ubi-io-inv(apebs1), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m, false)), ubi-io-peb-inv(mkpeb(aehdr0, avhdr0, buf3, m2, false)), unique-sqns(apebs1), unique-sqns(apebs0), valid-ebatbl(apebs1, wlar, vols, vtblpnum1), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs1, q), valid-eraseq(apebs0, q), valid-global-sqn(apebs1, sqnum), valid-global-sqn(apebs0, sqnum), valid-peb(v, vtblpnum4, mkpeb(aehdr0, avhdr0, buf3, m2, false)), valid-peb(v, vtblpnum4, mkpeb(aehdr, avhdr, buf2, m, false)), valid-peb(mkpeb(aehdr, avhdr, buf2, m, false)), valid-peb(mkpeb(aehdr0, avhdr0, buf3, m2, false)), valid-vtbl(apebs1, vols, wlar, vtblpnum1), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs1, wlar), valid-wl(apebs0, wlar), v ∈ vols, m ≤ vtblpnum3, n1 + n2 ≤ # buf, vtblpnum3 + n2 ≤ LEB_SIZE, vtblpnum3 ≤ LEB_SIZE, m ≤ LEB_SIZE, ⌊err0⌋ ⊦ err1 = ESUCCESS, m0 = vtblpnum1, n2 = 0, VTBL_VOLID ∈ vols, m0 ∈ q, vtblpnum1 ∈ q, ∃ buf0. # buf0 = vtblpnum3 + n2 ∧ range=(buf0, vtblpnum3, mkbuf(vtblpnum3 + n2), vtblpnum3, n2)

User applied rule exists right

And closed the goal!

Rule argument

pos: right 7 terms: mkbuf(vtblpnum3 + n2) abort: F discard: T computed: F

Additional information

Used simplifier rules: ⊦ # mkbuf(n) = n; (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% ⊦ range=(buf, n, buf, n, m) ↔ n + m ≤ # buf; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m; (s) Used terms: mkbuf(vtblpnum3 + n2)