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Proof step 108 from proof synced-write-buf (previous step)

# lpt = # avol, avol[m1] = mapped(buf0), n < n2, m1 < # avol, n < # buf, n0 < n2, n0 < # buf, awbuf-inv(avol, buffered(m1)), is-aligned(# buf0 + n0, EB_PAGE_SIZE), 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⌋ ⊦ ⟨avol[buffered(m1).leb] := mapped(avol[buffered(m1).leb].data + subarray(buf, 0, n)); isbuf := true⟩ (synced(avol) ∧ avol0 ↓ avol), n = 0, n0 = 0, synced(avol) ∧ avol0 ↓ avol

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 109:
# lpt = # avol, avol[m1] = mapped(buf0), buffered(m1).isbuf?, avol[buffered(m1).leb].mapped?, buffered(m1).leb < # avol, n0 < # buf, n0 < n2, n < # buf, m1 < # avol, n < n2, awbuf-inv(avol, buffered(m1)), is-aligned(# buf0 + n, EB_PAGE_SIZE), is-aligned(# buf0 + n0, EB_PAGE_SIZE), avol0 ↓ avol[m1, mapped(buf0 + subarray(buf, 0, n))], 0 + n ≤ # buf, n2 ≤ # buf, # buf0 + n2 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ # buf0 % EB_PAGE_SIZE + n, ⌊err2⌋ ⊦ ⟨isbuf := true⟩ ( synced(avol[buffered(m1).leb, mapped(avol[buffered(m1).leb].data + subarray(buf, 0, n))]) ∧ avol0 ↓ avol[buffered(m1).leb, mapped(avol[buffered(m1).leb].data + subarray(buf, 0, n))]), n = 0, n0 = 0, synced(avol) ∧ avol0 ↓ avol

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% ⊦ m < n → m ≤ n; (s)% ⊦ aleb.mapped? ↔ aleb ≠ unmapped; (ss)% ⊦ unmapped ≠ mapped(buf); (s)