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Proof step 120 from proof synced-write-buf (previous step)

# lpt = # avol, avol[m1] = mapped(buf0), n < n2, m1 < # avol, n < # buf, awbuf-inv(avol, buffered(m1)), is-aligned(# buf0 + n, EB_PAGE_SIZE), avol0 ↓ avol[m1, mapped(buf0 + subarray(buf, 0, n))], EB_PAGE_SIZE ≤ # buf0 % EB_PAGE_SIZE + n, # buf0 + n2 ≤ LEB_SIZE, n2 ≤ # buf, ⌊err2⌋ ⊦ n = 0, buffered(m1).isbuf?

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%n < # avol0, # buf0 < EB_PAGE_SIZE ⊦ avol0[n] = mapped(buf) ∧ is-aligned(# buf, EB_PAGE_SIZE) → (avol1 ↓ avol0[n, mapped(buf + buf0)] ↔ avol1 ↓ avol0); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ n + 0 = n; (s)%m ≠ 0 ⊦ is-aligned(n, m) → n % m = 0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ buffered(m).isbuf?; (s)