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Proof step 2 from proof synced-down-synced (previous step)

synced(avol0), avol1 ↓ avol0 ⊦ synced(avol1) ↔ true

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# avol1 = # avol0, avol1[n] = mapped(buf), n < # avol0, ∀ n. n < # avol0 ∧ avol0[n].mapped? → is-aligned(# avol0[n].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)) ⊦ is-aligned(# buf, EB_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: synced: ⊦ synced(avol) ↔ (∀ n. n < # avol ∧ avol[n].mapped? → is-aligned(# avol[n].data, EB_PAGE_SIZE));%down-arrow-def: ⊦ avol1 ↓ avol0 ↔ # avol1 = # avol0 ∧ (∀ n. n < # avol0 → avol1[n] ↓ avol0[n]);%down-arrow-block-def: ⊦ aleb1 ↓ aleb0 ↔ (aleb0.mapped? → aleb1 = mapped(aleb0.data.align↓)) ∧ ( ¬ aleb0.mapped? ∧ aleb1.mapped? → # aleb1.data ≤ LEB_SIZE ∧ is-aligned(# aleb1.data, EB_PAGE_SIZE));%down-arrow-buf: ⊦ buf.align↓ = subarray(buf, 0, align↓(# buf, EB_PAGE_SIZE));% ⊦ 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)