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Proof step 2 from proof crash-neutral-write (previous step)

# lpt = # avol, adr = adr0, lpt0 = lpt, m1 = m2, ns = ns0, plog = plog0, avol[m].mapped?, m < # avol, ebm-vol-inv(avol), is-aligned(n, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), n0 + n ≤ # buf, m0 + n ≤ LEB_SIZE, # avol[m].data ≤ m0, avol ⊆ avol0 ⊦ ⟨apersistence_io_write#(m, m0, n0, n, buf, adr0, m2, plog0, lpt, ns0; avol; err)⟩ (adr = adr0 ∧ m1 = m2 ∧ plog = plog0 ∧ lpt0 = lpt ∧ avol ⊆ avol0 ∧ ns = ns0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# lpt = # avol, avol[m] = mapped(buf0), m < # avol, ebm-vol-inv(avol), is-aligned(n, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), n0 + n ≤ # buf, m0 + n ≤ LEB_SIZE, # buf0 ≤ m0, avol ⊆ avol0 ⊦ ⟨apersistence_io_write#(m, m0, n0, n, buf, adr0, m2, plog0, lpt, ns0; avol; err)⟩ (avol ⊆ avol0)

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf).data = buf; (s)% ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)