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Proof step 55 from proof prepost-read-log (previous step)

# buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + logoff0, LEB_SIZE = n0 + # buf0, avol[m5] = mapped(buf0), copy(buf0 + mkempbuf(n0), logoff0, buf2, 0, EB_PAGE_SIZE) ≠ emptypage, n1 ≠ 0, m5 < # avol, logoff0 < LEB_SIZE, ebm-vol-inv(avol), is-aligned(logoff0, EB_PAGE_SIZE), is-encoded(log0, buf0), is-encoded(log, subarray(buf0, 0, logoff0)), logoff0 + EB_PAGE_SIZE ≤ LEB_SIZE, logoff0 ≤ # buf0, # buf0 ≤ LEB_SIZE ⊦ ⟪decode_ref_node#(EB_PAGE_SIZE, copy(avol[m5].data + mkempbuf(LEB_SIZE - # avol[m5].data), logoff0, buf2, 0, EB_PAGE_SIZE); rnd; err0); if err0 = ESUCCESS then log := log + rnd.leb '; logoff := logoff0 + EB_PAGE_SIZE⟫ ( logoff ≤ LEB_SIZE ∧ is-aligned(logoff, EB_PAGE_SIZE) ∧ (err0 = ESUCCESS ∨ err0 = ENOENT ∨ ⌊err0⌋ ) ∧ avol[m5].mapped? ∧ (err0 = ESUCCESS → logoff ≤ # avol[m5].data ∧ is-encoded(log, subarray(avol[m5].data, 0, logoff))) ∧ (err0 = ENOENT → is-encoded(log, avol[m5].data)) ∧ LEB_SIZE < n1 + logoff)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 56:
# buf2 = EB_PAGE_SIZE, LEB_SIZE = n0 + # buf0, LEB_SIZE = n1 + logoff0, LEB_SIZE = n2 + # avol[m5].data, avol[m5] = mapped(buf0), 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, # avol[m5].data ≤ LEB_SIZE ⊦ ⟪decode_ref_node#(EB_PAGE_SIZE, copy(avol[m5].data + mkempbuf(n2), logoff0, buf2, 0, EB_PAGE_SIZE); rnd; err0); if err0 = ESUCCESS then log := log + rnd.leb '; logoff := logoff0 + EB_PAGE_SIZE⟫ ( logoff ≤ LEB_SIZE ∧ is-aligned(logoff, EB_PAGE_SIZE) ∧ (err0 = ESUCCESS ∨ err0 = ENOENT ∨ ⌊err0⌋ ) ∧ avol[m5].mapped? ∧ (err0 = ESUCCESS → logoff ≤ # avol[m5].data ∧ is-encoded(log, subarray(avol[m5].data, 0, logoff))) ∧ (err0 = ENOENT → is-encoded(log, avol[m5].data)) ∧ LEB_SIZE < n1 + logoff), copy(buf0 + mkempbuf(n0), logoff0, buf2, 0, EB_PAGE_SIZE) = emptypage, n1 = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [# avol[m5].data, LEB_SIZE, n]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ mapped(buf).data = buf; (s)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ m + n < m; (s)%# buf ≤ n, n + m1 ≤ # buf + # buf0 ⊦ copy(buf + buf0, n, buf1, m0, m1) = copy(buf0, n - # buf, buf1, m0, m1); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # avol[m5].data, LEB_SIZE, n