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Proof step 7 from proof crash-neutral-unmap (previous step)

# lpt = # avol, m2 < # avol, awbuf-inv(avol, bleb), synced(avol), synced(avol0), avol0 ↓ avol ⊦ buffered(m2) = bleb, avol0 ↓ avol[m2, unmapped]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ avol1 ↓ avol0 ↔ # avol1 = # avol0 ∧ (∀ n. n < # avol0 → avol1[n] ↓ avol0[n])
Proof step 9:
# lpt = # avol, m2 < # avol, awbuf-inv(avol, bleb), synced(avol0), synced(avol), avol0 ↓ avol ⊦ buffered(m2) = bleb, # avol0 = # avol[m2, unmapped] ∧ (∀ n. n < # avol[m2, unmapped] → avol0[n] ↓ avol[m2, unmapped][n])

Rule argument

spec: awbuf-inv name: down-arrow-def seq: ⊦ avol1 ↓ avol0 ↔ # avol1 = # avol0 ∧ (∀ n. n < # avol0 → avol1[n] ↓ avol0[n]) subst: [avol0, avol1] → [avol[m2, unmapped], avol0] flags: <all paths>

Additional information

Used terms: avol[m2, unmapped], avol0