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Proof step 21 from proof recovery (previous step)

# buf = EB_PAGE_SIZE, # lpt1 = # avol2, # avol0 = # avol2, abs(avol2, bleb0, mkwbuf(buf, m2, m3), avol0, rofs0), awbuf-inv(avol2, bleb0), ebm-vol-inv(avol0), avol0 ⊆ avol1, bleb0 ≠ nobuffer → bleb0.leb < # avol2 ∧ wbuf-cons(mkwbuf(buf, m2, m3), avol0[bleb0.leb], rofs0) ⊦ avol1 ↓ avol2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ avol1 ↓ avol0 ↔ # avol1 = # avol0 ∧ (∀ n. n < # avol0 → avol1[n] ↓ avol0[n])
Proof step 23:
# avol0 = # avol2, # lpt1 = # avol2, # buf = EB_PAGE_SIZE, abs(avol2, bleb0, mkwbuf(buf, m2, m3), avol0, rofs0), awbuf-inv(avol2, bleb0), ebm-vol-inv(avol0), avol0 ⊆ avol1, bleb0 ≠ nobuffer → bleb0.leb < # avol2 ∧ wbuf-cons(mkwbuf(buf, m2, m3), avol0[bleb0.leb], rofs0) ⊦ # avol1 = # avol2 ∧ (∀ n. n < # avol2 → avol1[n] ↓ avol2[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] → [avol2, avol1] flags: <all paths>

Additional information

Used terms: avol2, avol1