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Proof step 174 from proof refine-write-data (previous step)

apebs[m3] = mkpeb(aehdr, avhdr, buf0, m2, false), avhdr.valid?, aehdr.valid?, m3 < # pebs, m3 < # apebs, abs(pebs, apebs), is-aligned(n1, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), n2 + n1 ≤ # buf, m0 + n1 ≤ LEB_SIZE, m2 ≤ m0 ⊦ pebs[m3].fill ≤ m0 + 2 * EB_PAGE_SIZE ∧ ¬ pebs[m3].bad

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: peb name: elim seq: ⊦ (buf = peb.data ∧ m = peb.fill) ∧ (boolvar ↔ peb.bad) ↔ peb = mkpeb(buf, m, boolvar) subst: [peb, buf, m, boolvar] → [pebs[m3], buf1, m, boolvar]

Additional information

Used simplifier rules: abs-bad: ⊦ n < # apebs ∧ abs(pebs, apebs) ∧ pebs[n] = mkpeb(buf0, m0, boolvar0) ∧ apebs[n] = mkpeb(aehdr, avhdr, buf, m1, boolvar1) → (boolvar0 ↔ boolvar1); (forward) from specification ubi-io-abs%abs-fwd: ⊦ n < # pebs ∧ pebs[n] = peb ∧ abs(pebs, apebs) → n < # apebs ∧ abs-peb(peb, apebs[n]); (forward) from specification ubi-io-abs% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%abs-fillcount-valid-headers: ⊦ n < # pebs ∧ apebs[n] = mkpeb(aehdr, avhdr, buf, m0, false) ∧ pebs[n] = mkpeb(buf0, m1, false) ∧ aehdr.valid? ∧ avhdr.valid? ∧ abs(pebs, apebs) → m1 = 2 * EB_PAGE_SIZE + m0; (forward) from specification ubi-io-abs% ⊦ m < n → n ≠ 0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%⊦ (buf = peb.data ∧ m = peb.fill) ∧ (boolvar ↔ peb.bad) ↔ peb = mkpeb(buf, m, boolvar); (elim) Used terms: pebs[m3], buf1, m, boolvar