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Proof step 93 from proof refine-write-data-wl (previous step)

apebs[m1] = mkpeb(aehdr, avhdr, buf2, 0, false), pebs[m1] = mkpeb(buf3, 2 * EB_PAGE_SIZE, false), n = align↑(datasize(buf, n), EB_PAGE_SIZE), n2 ≠ 0, avhdr.valid?, aehdr.valid?, m1 < # apebs, m1 < # pebs, n2 < n, n2 < LEB_SIZE, n2 < # buf, n2 < datasize(buf, n), abs(pebs, apebs), abs-peb(mkpeb(buf3, 2 * EB_PAGE_SIZE, false), mkpeb(aehdr, avhdr, buf2, 0, false)), is-aligned(n2, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), 2 * EB_PAGE_SIZE + n2 ≤ PEB_SIZE, n ≤ LEB_SIZE, n ≤ # buf, ⌊err1⌋ ⊦ ( datasize(subarray(buf, 0, n2), n2) < datasize(buf, n) ∨ checksum(buf + mkempbuf(n - # buf), datasize(buf, n)) ≠ checksum(buf, datasize(buf, n))) ∧ ⟨apebs[m1] := mkpeb (apebs[m1].echdr, apebs[m1].vidhdr, subarray(buf, 0, n2) + mkempbuf(LEB_SIZE - # subarray(buf, 0, n2)), # subarray(buf, 0, n2), apebs[m1].bad)⟩ abs(pebs[m1, (pebs[m1].data:= copy(buf, 0, pebs[m1].data, 2 * EB_PAGE_SIZE, n2)).fill:= (2 * EB_PAGE_SIZE + n2)], apebs)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 94:
LEB_SIZE = n0 + # subarray(buf, 0, n2), pebs[m1] = mkpeb(buf3, 2 * EB_PAGE_SIZE, false), apebs[m1] = mkpeb(aehdr, avhdr, buf2, 0, false), n = align↑(datasize(buf, n), EB_PAGE_SIZE), aehdr.valid?, avhdr.valid?, n2 < datasize(buf, n), n2 < # buf, n2 < LEB_SIZE, n2 < n, m1 < # pebs, m1 < # apebs, abs(pebs, apebs), abs-peb(mkpeb(buf3, 2 * EB_PAGE_SIZE, false), mkpeb(aehdr, avhdr, buf2, 0, false)), is-aligned(n, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), n ≤ # buf, n ≤ LEB_SIZE, 2 * EB_PAGE_SIZE + n2 ≤ PEB_SIZE, # subarray(buf, 0, n2) ≤ LEB_SIZE, ⌊err1⌋ ⊦ ( datasize(subarray(buf, 0, n2), n2) < datasize(buf, n) ∨ checksum(buf + mkempbuf(n - # buf), datasize(buf, n)) ≠ checksum(buf, datasize(buf, n))) ∧ ⟨apebs[m1] := mkpeb(apebs[m1].echdr, apebs[m1].vidhdr, subarray(buf, 0, n2) + mkempbuf(n0), # subarray(buf, 0, n2), apebs[m1].bad)⟩ abs(pebs[m1, (pebs[m1].data:= copy(buf, 0, pebs[m1].data, 2 * EB_PAGE_SIZE, n2)).fill:= (2 * EB_PAGE_SIZE + n2)], apebs), n2 = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [# subarray(buf, 0, n2), LEB_SIZE, n0]

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ m < n → m ≤ n; (s)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # subarray(buf, 0, n2), LEB_SIZE, n0