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Proof step 119 from proof synced-write-buf (previous step)

# lpt = # avol, avol[m1] = mapped(buf0), buffered(m1).isbuf?, avol[buffered(m1).leb].mapped?, buffered(m1).leb < # avol, 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))], 0 + n ≤ # buf, EB_PAGE_SIZE ≤ # buf0 % EB_PAGE_SIZE + n, # buf0 + n2 ≤ LEB_SIZE, n2 ≤ # buf, ⌊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, synced(avol) ∧ avol0 ↓ avol

Heuristic symbolic execution applied rule assign right

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ 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)% ⊦ buffered(m).leb = m; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ buffered(m).isbuf?; (s)%⊦ awbuf-inv(avol, buffered(n)) → (synced(avol[n, mapped(buf)]) ↔ is-aligned(# buf, EB_PAGE_SIZE)); (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # subarray(buf, m, n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ mapped(buf).data = buf; (s)