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Proof step 35 from proof inv-write-data (previous step)

LEB_SIZE = (n0 + n2) + n5, apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false), aehdr.valid?, avhdr.valid?, n < # apebs, n2 < n4, is-aligned(n2, EB_PAGE_SIZE), is-aligned(n5, EB_PAGE_SIZE), is-aligned(n4, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf0, m, false)), n1 + n2 ≤ # buf, m ≤ n5, n5 + n4 ≤ LEB_SIZE, n1 + n4 ≤ # buf, m ≤ LEB_SIZE, n5 ≤ LEB_SIZE, n2 + n5 ≤ LEB_SIZE, ⌊err0⌋ ⊦ n2 = 0, (aehdr = empty → avhdr = empty) ∧ (aehdr ≠ garbage ∧ avhdr = empty → n5 + n2 = 0) ∧ subarray(mkempbuf(n0), 0, LEB_SIZE - n5 + n2) = mkempbuf(LEB_SIZE - n5 + n2)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 36:
LEB_SIZE = (n0 + n2) + n5, LEB_SIZE = n3 + n5 + n2, apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false), avhdr.valid?, aehdr.valid?, n2 < n4, n < # apebs, is-aligned(n4, EB_PAGE_SIZE), is-aligned(n5, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf0, m, false)), n2 + n5 ≤ LEB_SIZE, n5 ≤ LEB_SIZE, m ≤ LEB_SIZE, n1 + n4 ≤ # buf, n5 + n4 ≤ LEB_SIZE, m ≤ n5, n1 + n2 ≤ # buf, n5 + n2 ≤ LEB_SIZE, ⌊err0⌋ ⊦ n2 = 0, (aehdr = empty → avhdr = empty) ∧ (aehdr ≠ garbage ∧ avhdr = empty → n5 + n2 = 0) ∧ subarray(mkempbuf(n0), 0, n3) = mkempbuf(n3)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [LEB_SIZE, n5 + n2, n3]

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: LEB_SIZE, n5 + n2, n3