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Proof step 17 from proof crash-neutral-unmap (previous step)

# lpt = # avol, # avol0 = # avol, n < # avol, m2 < # avol, awbuf-inv(avol, bleb), synced(avol0), synced(avol), avol0[n] ↓ avol[n] ⊦ buffered(m2) = bleb, (avol[m2, unmapped][n].mapped? → avol0[n] = mapped(avol[m2, unmapped][n].data.align↓)) ∧ (¬ avol[m2, unmapped][n].mapped? ∧ avol0[n].mapped? → # avol0[n].data ≤ LEB_SIZE ∧ is-aligned(# avol0[n].data, EB_PAGE_SIZE))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ aleb1 ↓ aleb0 ↔ (aleb0.mapped? → aleb1 = mapped(aleb0.data.align↓)) ∧ (¬ aleb0.mapped? ∧ aleb1.mapped? → # aleb1.data ≤ LEB_SIZE ∧ is-aligned(# aleb1.data, EB_PAGE_SIZE))
Proof step 19:
# avol0 = # avol, # lpt = # avol, m2 < # avol, n < # avol, awbuf-inv(avol, bleb), synced(avol), synced(avol0), avol[n].mapped? → avol0[n] = mapped(avol[n].data.align↓), ¬ avol[n].mapped? ∧ avol0[n].mapped? → # avol0[n].data ≤ LEB_SIZE ∧ is-aligned(# avol0[n].data, EB_PAGE_SIZE) ⊦ buffered(m2) = bleb, (avol[m2, unmapped][n].mapped? → avol0[n] = mapped(avol[m2, unmapped][n].data.align↓)) ∧ (¬ avol[m2, unmapped][n].mapped? ∧ avol0[n].mapped? → # avol0[n].data ≤ LEB_SIZE ∧ is-aligned(# avol0[n].data, EB_PAGE_SIZE))

Rule argument

spec: awbuf-inv name: down-arrow-block-def seq: ⊦ aleb1 ↓ aleb0 ↔ (aleb0.mapped? → aleb1 = mapped(aleb0.data.align↓)) ∧ ( ¬ aleb0.mapped? ∧ aleb1.mapped? → # aleb1.data ≤ LEB_SIZE ∧ is-aligned(# aleb1.data, EB_PAGE_SIZE)) subst: [aleb0, aleb1] → [avol[n], avol0[n]] flags: <all paths>

Additional information

Used terms: avol[n], avol0[n]