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Proof step 241 from proof refine-write (previous step)

# apebs0 = # wlar, LEB_SIZE - vtblpnum5 = n1 + n2, LEB_SIZE = (n0 + n2) + vtblpnum5, apebs0[n4] = mkpeb(aehdr, avhdr, buf2, m0, false), wlar[n4] = wl-entry(m1, used), avols2[v][vtblpnum3] = mapped(buf2, m), vols[v][vtblpnum3] = ⌜n4⌝ , avhdr.valid?, aehdr.valid?, vtblpnum3 < # avols2[v], n4 < # wlar, vtblpnum3 < # vols[v], n2 < n5, abs(avols2, apebs0, vols, q), abs (avols2[v, avols2[v][vtblpnum3, mapped(subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2)]], apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)], vols, q), abs(avols2[v, avols2[v][vtblpnum3, mapped(subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2)]], apebs1, vols0, q0), bflipset-cons(bflipset, wlar), ebm-cons(avols2), ebm-cons(avols2[v, avols2[v][vtblpnum3, mapped(subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2)]]), is-aligned(vtblpnum5, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), is-aligned(n5, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)]), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m0, false)), unique-sqns(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)]), unique-sqns(apebs0), valid-ebatbl (apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)], wlar, vols, vtblpnum4), valid-ebatbl(apebs0, wlar, vols, vtblpnum4), valid-eraseq(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)], q), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)], sqnum), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum4), valid-wl(apebs0[n4, mkpeb(aehdr, avhdr, subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n0), vtblpnum5 + n2, false)], wlar), valid-wl(apebs0, wlar), v ∈ avols2, v ∈ vols, vtblpnum5 + n5 ≤ LEB_SIZE, m0 ≤ vtblpnum5, m ≤ vtblpnum5, n5 + n3 ≤ # buf0, n3 + n2 ≤ # buf0, n3 + n5 ≤ # buf0, m0 ≤ LEB_SIZE, m ≤ LEB_SIZE, vtblpnum5 ≤ LEB_SIZE, n2 + vtblpnum5 ≤ LEB_SIZE, ⌊err2⌋ , ⌊err3⌋ ⊦ n2 = 0, vtblpnum4 = n4, abs(avols2, apebs1, vols0, q0), abs (avols2[v, avols2[v][vtblpnum3, mapped(subarray(buf2, 0, vtblpnum5) + subarray(buf0, n3, n2) + mkempbuf(n1), vtblpnum5 + n2)]], apebs1, vols0, q0), VTBL_VOLID ∈ vols

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [vtblpnum5, LEB_SIZE, n]

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: vtblpnum5, LEB_SIZE, n