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Proof step 65 from proof prepost-read-log (previous step)

# buf2 = EB_PAGE_SIZE, LEB_SIZE = n0 + # buf0, LEB_SIZE = n1 + logoff0, avol[m5] = mapped(buf0), err = ESUCCESS, logoff0 < LEB_SIZE, m5 < # avol, ebm-vol-inv(avol), is-aligned(logoff0, EB_PAGE_SIZE), is-encoded(log, subarray(buf0, 0, logoff0)), is-encoded(log0, buf0), # buf0 ≤ LEB_SIZE, logoff0 ≤ # buf0, logoff0 + EB_PAGE_SIZE ≤ LEB_SIZE, err = ESUCCESS → is-encoded(rnd, subarray(buf0 + mkempbuf(n0), logoff0, EB_PAGE_SIZE)), err = ESUCCESS ∨ ⌊err⌋ ⊦ copy(buf0 + mkempbuf(n0), logoff0, buf2, 0, EB_PAGE_SIZE) = emptypage, n1 = 0, logoff0 + EB_PAGE_SIZE ≤ LEB_SIZE ∧ is-aligned(logoff0 + EB_PAGE_SIZE, EB_PAGE_SIZE) ∧ (err = ESUCCESS ∨ err = ENOENT ∨ ⌊err⌋ ) ∧ avol[m5].mapped? ∧ (err = ESUCCESS → logoff0 + EB_PAGE_SIZE ≤ # avol[m5].data ∧ is-encoded(log + rnd.leb ', subarray(avol[m5].data, 0, logoff0 + EB_PAGE_SIZE))) ∧ (err = ENOENT → is-encoded(log + rnd.leb ', avol[m5].data)) ∧ LEB_SIZE < n1 + logoff0 + EB_PAGE_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 66:
# buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + logoff0, LEB_SIZE = n0 + # buf0, avol[m5] = mapped(buf0), m5 < # avol, logoff0 < LEB_SIZE, LEB_SIZE < n1 + logoff0 + EB_PAGE_SIZE, # buf0 < n1 + logoff0 + EB_PAGE_SIZE, ebm-vol-inv(avol), is-aligned(logoff0, EB_PAGE_SIZE), is-encoded(log0, buf0), is-encoded(log, subarray(buf0, 0, logoff0)), is-encoded(rnd, subarray(buf0 + mkempbuf(n0), logoff0, EB_PAGE_SIZE)), logoff0 + EB_PAGE_SIZE ≤ LEB_SIZE, logoff0 ≤ # buf0, # buf0 ≤ LEB_SIZE ⊦ copy(buf0 + mkempbuf(n0), logoff0, buf2, 0, EB_PAGE_SIZE) = emptypage, n1 = 0, is-encoded(log + rnd.leb ', subarray(buf0, 0, logoff0 + EB_PAGE_SIZE)) ∧ logoff0 + EB_PAGE_SIZE ≤ # buf0

Rule argument

Additional information

Used simplifier rules: nat-stuff1: ⊦ n = n0 + n1 → (n0 + n1 + n2 ≤ n ↔ n2 = 0);% ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1; (ws)% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)% ⊦ m +1 = m + 1; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ EB_PAGE_SIZE + n = 0 ↔ false; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ # subarray(buf, m, n) = n; (s)%is-encoded-size: ⊦ is-encoded(rnd, buf) → # buf = EB_PAGE_SIZE; (forward) from specification encoding-page-size-nonempty[encoding-ref-node]% ⊦ ESUCCESS ≠ ENOENT; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%n ≠ 0 ⊦ is-aligned(n, n); (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)