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Proof step 32 from proof prepost-read-log (previous step)

# buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + logoff0, avol[m5] = mapped(buf0), buf = mkempbuf(# buf), buf = copy(avol[m5].data + mkempbuf(LEB_SIZE - # avol[m5].data), logoff0, buf1, 0, EB_PAGE_SIZE), buf1 = buf2, err = err0, err = ESUCCESS, m0 = EB_PAGE_SIZE, avol[m5].mapped?, 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), logoff0 ≤ # buf0, logoff0 + EB_PAGE_SIZE ≤ LEB_SIZE, logoff0 + EB_PAGE_SIZE ≤ #(avol[m5].data + mkempbuf(LEB_SIZE - # avol[m5].data)), 0 + EB_PAGE_SIZE ≤ # buf1, LEB_SIZE ≥ # avol[m5].data, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ n1 = 0, logoff0 + m0 ≤ LEB_SIZE ∧ # buf = m0 ∧ is-aligned(logoff0 + m0, # buf) ∧ (ENOENT = ESUCCESS ∨ ENOENT = ENOENT ∨ ⌊ENOENT⌋ ) ∧ avol[m5].mapped? ∧ (ENOENT = ESUCCESS → logoff0 + m0 ≤ # avol[m5].data ∧ is-encoded(log, subarray(avol[m5].data, 0, logoff0 + m0))) ∧ (ENOENT = ENOENT → is-encoded(log, avol[m5].data)) ∧ LEB_SIZE < n1 + logoff0 + m0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
# buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + logoff0, avol[m5] = mapped(buf0), copy(buf0 + mkempbuf(LEB_SIZE - # buf0), logoff0, buf2, 0, EB_PAGE_SIZE) = emptypage, LEB_SIZE < n1 + logoff0 + EB_PAGE_SIZE, m5 < # avol, logoff0 < LEB_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)), # buf0 ≤ LEB_SIZE, logoff0 + EB_PAGE_SIZE ≤ # buf0 + (LEB_SIZE - # buf0), logoff0 + EB_PAGE_SIZE ≤ LEB_SIZE, logoff0 ≤ # buf0 ⊦ log0 = log, n1 = 0

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 < n → m ≤ n; (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%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%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)% ⊦ is-encoded(nx0, buf) → (is-encoded(nx1, buf) ↔ nx0 = nx1); (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ m ≤ m; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ mkempbuf(EB_PAGE_SIZE) = emptypage; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ ESUCCESS ≠ ENOENT; (s)%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)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkempbuf(n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ # copy(buf, m, buf0, m0, n) = # buf0; (s)