[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 19 from proof prepost-read-log (previous step)

# buf = EB_PAGE_SIZE, LEB_SIZE = n1 + logoff0, avol[m5] = mapped(buf1), buf0 = buf, m = logoff0, m0 = m5, n = EB_PAGE_SIZE, n0 = 0, avol[m0].mapped?, m0 < # avol, m5 < # avol, logoff0 < LEB_SIZE, ebm-vol-inv(avol), is-aligned(logoff0, EB_PAGE_SIZE), is-encoded(log0, buf1), is-encoded(log, subarray(buf1, 0, logoff0)), n0 + n ≤ # buf0, m + n ≤ LEB_SIZE, logoff0 ≤ # buf1, m0 < # avol → m0 < # avol ⊦ ⟪fail_or_success#(; ; err); if err = ESUCCESS then buf0 := copy(avol[m0].data + mkempbuf(LEB_SIZE - # avol[m0].data), m, buf0, n0, n) else choose buf with # buf = # buf0 ∧ range=(buf0, 0, buf, 0, n0) ∧ range=(buf0, n0 + n, buf, n0 + n, # buf0 - n0 + n) in buf0 := buf; m0 := EB_PAGE_SIZE; buf := buf0; if err = ESUCCESS then if buf = mkempbuf(# buf) then err := ENOENT else let rnd = ? in {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), n1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
# buf = EB_PAGE_SIZE, LEB_SIZE = n1 + logoff0, avol[m5] = mapped(buf1), n1 ≠ 0, logoff0 < LEB_SIZE, m5 < # avol, ebm-vol-inv(avol), is-aligned(logoff0, EB_PAGE_SIZE), is-encoded(log, subarray(buf1, 0, logoff0)), is-encoded(log0, buf1), logoff0 ≤ # buf1, logoff0 + EB_PAGE_SIZE ≤ LEB_SIZE ⊦ ⟪fail_or_success#(; ; err); buf1 := buf; if err = ESUCCESS then buf1 := copy(avol[m5].data + mkempbuf(LEB_SIZE - # avol[m5].data), logoff0, buf1, 0, EB_PAGE_SIZE) else {n0 := 0; n := EB_PAGE_SIZE; choose buf with # buf = # buf1 ∧ range=(buf1, 0, buf, 0, n0) ∧ range=(buf1, n0 + n, buf, n0 + n, # buf1 - n0 + n) in buf1 := buf}; m0 := EB_PAGE_SIZE; buf := buf1; if err = ESUCCESS then if buf = mkempbuf(# buf) then err := ENOENT else let rnd = ? in {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)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ 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)