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Proof step 10 from proof refine-read-data (previous step)

apebs[m3] = mkpeb(aehdr, avhdr, buf1, m2, false), pebs[m3] = mkpeb(buf2, m, false), buf = buf0, m3 < # apebs, m3 < # pebs, abs(pebs, apebs), abs-peb(mkpeb(buf2, m, false), mkpeb(aehdr, avhdr, buf1, m2, false)), mtd-cons(pebs), ubi-io-inv(apebs), m0 + n1 ≤ LEB_SIZE, n2 + n1 ≤ # buf0 ⊦ ⟪ubi_io_read#(m3, m0 + 2 * EB_PAGE_SIZE, n2, n1, pebs; buf; bitflips, err)⟫ ⟨aubi_io_read_data#(m3, m0, n2, n1, apebs; buf0; isbad, err0)⟩ (buf = buf0 ∧ (bitflips ↔ isbad) ∧ err = err0)

User applied rule insert program lemma

And obtained the following new goals

Proof step 11:
mtd-cons(pebs), m < # pebs, ¬ pebs[m].bad, m0 + n ≤ PEB_SIZE, n0 + n ≤ # buf, buf0 = buf ⊦ ⟪ubi_io_read#(m, m0, n0, n, pebs; buf; bitflips, err)⟫ ( # buf = # buf0 ∧ range=(buf, 0, buf0, 0, n0) ∧ range=(buf, n0 + n, buf0, n0 + n, # buf0 - n0 + n) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → subarray(buf, n0, n) = subarray(pebs[m].data, m0, n)))
Proof step 12:
pebs[m3] = mkpeb(buf2, m, false), apebs[m3] = mkpeb(aehdr, avhdr, buf1, m2, false), buf = buf0, buf = buf, buf3 = buf, m1 = m3, m4 = m0 + 2 * EB_PAGE_SIZE, n3 = n1, n4 = n2, pebs0 = pebs, m3 < # apebs, m3 < # pebs, abs(pebs, apebs), abs-peb(mkpeb(buf2, m, false), mkpeb(aehdr, avhdr, buf1, m2, false)), mtd-cons(pebs), ubi-io-inv(apebs), n2 + n1 ≤ # buf0, m0 + n1 ≤ LEB_SIZE, (m0 + 2 * EB_PAGE_SIZE) + n1 ≤ PEB_SIZE, n2 + n1 ≤ # buf ⊦ [ubi_io_read#(m3, m0 + 2 * EB_PAGE_SIZE, n2, n1, pebs; buf; bitflips, err)] ( # buf = # buf3 ∧ range=(buf, 0, buf3, 0, n4) ∧ range=(buf, n4 + n3, buf3, n4 + n3, # buf3 - n4 + n3) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → subarray(buf, n4, n3) = subarray(pebs0[m1].data, m4, n3)) → ⟨aubi_io_read_data#(m3, m0, n2, n1, apebs; buf0; isbad, err0)⟩ (buf = buf0 ∧ (bitflips ↔ isbad) ∧ err = err0)), pebs[m3].bad

Rule argument

spec: ubi-io-asm name: inv-io-read seq: mtd-cons(pebs), m < # pebs, ¬ pebs[m].bad, m0 + n ≤ PEB_SIZE, n0 + n ≤ # buf, buf0 = buf ⊦ ⟪ubi_io_read#(m, m0, n0, n, pebs; buf; bitflips, err)⟫ ( # buf = # buf0 ∧ range=(buf, 0, buf0, 0, n0) ∧ range=(buf, n0 + n, buf0, n0 + n, # buf0 - n0 + n) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → subarray(buf, n0, n) = subarray(pebs[m].data, m0, n))) subst: [pebs, n, n0, m0, m, buf, err, bitflips, buf0] → [pebs, n1, n2, m0 + 2 * EB_PAGE_SIZE, m3, buf, err, bitflips, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mkpeb(buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ LEB_SIZE → ¬ PEB_SIZE < m + 2 * EB_PAGE_SIZE; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic