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Proof step 25 from proof refine-destroy-buf (previous step)

# buf = EB_PAGE_SIZE, # lpt0 = # avol, # avol0 = # avol, avol0[m] = mapped(buf0), m < # avol, abs(avol, buffered(m), mkwbuf(buf, m2, m1), avol0, false), awbuf-inv(avol, buffered(m)), ebm-vol-inv(avol0), synced(avol), wbuf-cons(mkwbuf(buf, m2, m1), mapped(buf0), false) ⊦ avol = avol0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ avol = avol0 ↔ # avol = # avol0 ∧ (∀ n. n < # avol → avol[n] = avol0[n])
Proof step 27:
# avol0 = # avol, # lpt0 = # avol, # buf = EB_PAGE_SIZE, avol0[m] = mapped(buf0), m < # avol, abs(avol, buffered(m), mkwbuf(buf, m2, m1), avol0, false), awbuf-inv(avol, buffered(m)), ebm-vol-inv(avol0), synced(avol), wbuf-cons(mkwbuf(buf, m2, m1), mapped(buf0), false) ⊦ # avol = # avol0 ∧ (∀ n. n < # avol → avol[n] = avol0[n])

Rule argument

spec: array, inst: avolume name: Extension seq: ⊦ avol = avol0 ↔ # avol = # avol0 ∧ (∀ n. n < # avol → avol[n] = avol0[n]) subst: [avol0, avol] → [avol0, avol] flags: <all paths>

Additional information

Used terms: avol0, avol