[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 63 from proof synced-write-buf (previous step)

# lpt = # avol, # buf0 + n0 = align↓(# buf0 + n, EB_PAGE_SIZE), avol[m1] = mapped(buf0), m1 < # avol, awbuf-inv(avol, buffered(m1)), avol0 ↓ avol[m1, mapped(buf0 + subarray(buf, 0, n))], EB_PAGE_SIZE ≤ # buf0 % EB_PAGE_SIZE + n, # buf0 + n ≤ LEB_SIZE, n ≤ # buf, ¬ is-aligned(# buf0 + n, EB_PAGE_SIZE) ⊦ n0 ≠ 0 ∧ n0 < n ∧ is-aligned(# avol[m1].data + n0, EB_PAGE_SIZE) ∧ ⟨avol[buffered(m1).leb] := mapped(avol[buffered(m1).leb].data + subarray(buf, 0, n0)); isbuf := true⟩ (synced(avol) ∧ avol0 ↓ avol)

Heuristic dl case distinction applied rule case distinction

And obtained the following new goals

Proof step 64:
# lpt = # avol, # buf0 + n0 = align↓(# buf0 + n, EB_PAGE_SIZE), avol[m1] = mapped(buf0), m1 < # avol, awbuf-inv(avol, buffered(m1)), avol0 ↓ avol[m1, mapped(buf0 + subarray(buf, 0, n))], n ≤ # buf, # buf0 + n ≤ LEB_SIZE, EB_PAGE_SIZE ≤ # buf0 % EB_PAGE_SIZE + n ⊦ n0 < n, is-aligned(# buf0 + n, EB_PAGE_SIZE)
Proof step 67:
# lpt = # avol, # buf0 + n0 = align↓(# buf0 + n, EB_PAGE_SIZE), avol[m1] = mapped(buf0), m1 < # avol, awbuf-inv(avol, buffered(m1)), avol0 ↓ avol[m1, mapped(buf0 + subarray(buf, 0, n))], n ≤ # buf, # buf0 + n ≤ LEB_SIZE, EB_PAGE_SIZE ≤ # buf0 % EB_PAGE_SIZE + n ⊦ ⟨avol[buffered(m1).leb] := mapped(avol[buffered(m1).leb].data + subarray(buf, 0, n0)); isbuf := true⟩ (synced(avol) ∧ avol0 ↓ avol), is-aligned(# buf0 + n, EB_PAGE_SIZE)

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ mapped(buf).data = buf; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%m ≠ 0 ⊦ n = align↓(n0, m) → is-aligned(n, m); (ss)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%m ≠ 0 ⊦ align↓(n0 + n1, m) = n0 ↔ n1 < m ∧ is-aligned(n0, m); (ws)%m ≠ 0 ⊦ is-aligned(n, m) → n % m = 0; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)