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Proof step 4 from proof down-appended-less (previous step)

# avol1 = # avol0, avol0[n] = mapped(buf), n < # avol0, # buf0 < EB_PAGE_SIZE, is-aligned(# buf, EB_PAGE_SIZE), ∀ n0. n0 < # avol0 → ( avol0[n, mapped(buf + buf0)][n0].mapped? → avol1[n0] = mapped(subarray(avol0[n, mapped(buf + buf0)][n0].data, 0, align↓(# avol0[n, mapped(buf + buf0)][n0].data, EB_PAGE_SIZE)))) ∧ ( ¬ avol0[n, mapped(buf + buf0)][n0].mapped? ∧ avol1[n0].mapped? → # avol1[n0].data ≤ LEB_SIZE ∧ is-aligned(# avol1[n0].data, EB_PAGE_SIZE)) ⊦ ∀ n0. n0 < # avol0 → (avol0[n0].mapped? → avol1[n0] = mapped(subarray(avol0[n0].data, 0, align↓(# avol0[n0].data, EB_PAGE_SIZE)))) ∧ (¬ avol0[n0].mapped? ∧ avol1[n0].mapped? → # avol1[n0].data ≤ LEB_SIZE ∧ is-aligned(# avol1[n0].data, EB_PAGE_SIZE))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
# avol1 = # avol0, avol0[n] = mapped(buf), n < # avol0, # buf0 < EB_PAGE_SIZE, n0 < # avol0, is-aligned(# buf, EB_PAGE_SIZE), ∀ n0. n0 < # avol0 → ( avol0[n, mapped(buf + buf0)][n0].mapped? → avol1[n0] = mapped(subarray(avol0[n, mapped(buf + buf0)][n0].data, 0, align↓(# avol0[n, mapped(buf + buf0)][n0].data, EB_PAGE_SIZE)))) ∧ ( ¬ avol0[n, mapped(buf + buf0)][n0].mapped? ∧ avol1[n0].mapped? → # avol1[n0].data ≤ LEB_SIZE ∧ is-aligned(# avol1[n0].data, EB_PAGE_SIZE)) ⊦ (avol0[n0].mapped? → avol1[n0] = mapped(subarray(avol0[n0].data, 0, align↓(# avol0[n0].data, EB_PAGE_SIZE)))) ∧ (¬ avol0[n0].mapped? ∧ avol1[n0].mapped? → # avol1[n0].data ≤ LEB_SIZE ∧ is-aligned(# avol1[n0].data, EB_PAGE_SIZE))

Rule argument

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic