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Proof step 52 from proof prepost-read-log (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
# 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, n1 ≠ 0, 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, logoff0 + EB_PAGE_SIZE ≤ # buf0 + (LEB_SIZE - # buf0) ⊦ ⟪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)

Rule argument

Additional information

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