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Proof step 17 from proof inv-write-data-wl (previous step)

LEB_SIZE = n0 + n1, apebs[n2] = mkpeb(aehdr, avhdr, buf1, 0, false), n1 = align↑(datasize(buf, n1), EB_PAGE_SIZE), avhdr.valid?, aehdr.valid?, n2 < # apebs, ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf1, 0, false)), n1 ≤ LEB_SIZE, n1 ≤ # buf ⊦ datasize(buf, n1) = 0, (aehdr = empty → avhdr = empty) ∧ (aehdr ≠ garbage ∧ avhdr = empty → n1 = 0) ∧ is-aligned(n1, EB_PAGE_SIZE) ∧ subarray(mkempbuf(n0), 0, LEB_SIZE - n1) = mkempbuf(LEB_SIZE - n1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 18:
LEB_SIZE = n0 + n1, LEB_SIZE = n3 + n1, apebs[n2] = mkpeb(aehdr, avhdr, buf1, 0, false), n1 = align↑(datasize(buf, n1), EB_PAGE_SIZE), aehdr.valid?, avhdr.valid?, n2 < # apebs, ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf1, 0, false)), n1 ≤ # buf, n1 ≤ LEB_SIZE ⊦ datasize(buf, n1) = 0, (aehdr = empty → avhdr = empty) ∧ (aehdr ≠ garbage ∧ avhdr = empty → n1 = 0) ∧ is-aligned(n1, EB_PAGE_SIZE) ∧ 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, n1, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: LEB_SIZE, n1, n