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Proof step 67 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))], 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)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 68:
# lpt = # avol, # buf0 + n0 = align↓(# buf0 + n, EB_PAGE_SIZE), avol[m1] = mapped(buf0), buffered(m1).isbuf?, avol[buffered(m1).leb].mapped?, buffered(m1).leb < # avol, m1 < # avol, awbuf-inv(avol, buffered(m1)), avol0 ↓ avol[m1, mapped(buf0 + subarray(buf, 0, n))], 0 + n0 ≤ # buf, EB_PAGE_SIZE ≤ # buf0 % EB_PAGE_SIZE + n, # buf0 + n ≤ LEB_SIZE, n ≤ # buf ⊦ ⟨isbuf := true⟩ ( synced(avol[buffered(m1).leb, mapped(avol[buffered(m1).leb].data + subarray(buf, 0, n0))]) ∧ avol0 ↓ avol[buffered(m1).leb, mapped(avol[buffered(m1).leb].data + subarray(buf, 0, n0))]), is-aligned(# buf0 + n, EB_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: ⊦ buffered(m).leb = m; (s)% ⊦ buffered(m).isbuf?; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ mapped(buf).mapped?; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%m ≠ 0 ⊦ align↓(n0 + n1, m) = n2 + n1 → ¬ n0 < n2; (s)