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Proof step 8 from proof inv-write-data-wl (previous step)

pebs[m0] = mkpeb(buf0, 2 * EB_PAGE_SIZE, false), m0 < # pebs, is-aligned(n, EB_PAGE_SIZE), mtd-cons(pebs), n ≤ LEB_SIZE, n ≤ # buf ⊦ ⟪mtd_asm_write#(m0, 2 * EB_PAGE_SIZE, 0, n, buf; pebs; err)⟫ mtd-cons(pebs)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: mtd-asm name: inv-write seq: mtd-cons(pebs), m < # pebs, ¬ pebs[m].bad, pebs[m].fill ≤ m0, m0 + n ≤ PEB_SIZE, n0 + n ≤ # buf, is-aligned(m0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE) ⊦ ⟪mtd_asm_write#(m, m0, n0, n, buf; pebs; err)⟫ mtd-cons(pebs) subst: [buf, n, n0, m0, m, pebs, err] → [buf, n, 0, 2 * EB_PAGE_SIZE, m0, pebs, err] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ is-aligned(n0 * n, n); (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ mkpeb(buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ mkpeb(buf, m, boolvar).fill = m; (s)%0 ≠ m ⊦ (* m) * n ≤ m * n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ LEB_SIZE → ¬ PEB_SIZE < m + 2 * EB_PAGE_SIZE; (s)