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Proof step 45 from proof refine-read-data (previous step)

# buf3 = # buf0, # buf0 = n3 + n2 + n1, apebs[m3] = mkpeb(aehdr, avhdr, buf1, m2, false), pebs[m3] = mkpeb(buf2, m4, false), buf3[(n2 + n1) + (n - n2 + n1)] = buf0[(n2 + n1) + (n - n2 + n1)], subarray(buf3, n2, n1) = subarray(buf2, m1 + 2 * EB_PAGE_SIZE, n1), m3 < # pebs, m3 < # apebs, n < # buf0, n2 + n1 < # buf0, abs(pebs, apebs), abs-peb(mkpeb(buf2, m4, false), mkpeb(aehdr, avhdr, buf1, m2, false)), mtd-cons(pebs), range=(buf3, 0, buf0, 0, n2), ubi-io-inv(apebs), n2 + n1 ≤ n, (m1 + 2 * EB_PAGE_SIZE) + n1 ≤ PEB_SIZE, m1 + n1 ≤ LEB_SIZE ⊦ buf3[n] = buf0[n], n3 = 0

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: [m, n, n0] → [n, n2 + n1, n0]

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%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, n2 + n1, n0