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Proof step 27 from proof recovery (previous step)

# buf = EB_PAGE_SIZE, # lpt1 = # avol2, # avol1 = # avol2, # avol0 = # avol2, n < # avol2, abs(avol2, bleb0, mkwbuf(buf, m2, m3), avol0, rofs0), awbuf-inv(avol2, bleb0), ebm-vol-inv(avol0), bleb0 ≠ nobuffer → bleb0.leb < # avol2 ∧ wbuf-cons(mkwbuf(buf, m2, m3), avol0[bleb0.leb], rofs0), ∀ m. m < # avol2 → (avol0[m].mapped? → avol1[m] = avol0[m]) ∧ (avol0[m] = unmapped ∧ avol1[m].mapped? → # avol1[m].data ≤ LEB_SIZE ∧ is-aligned(# avol1[m].data, EB_PAGE_SIZE)) ⊦ avol1[n] ↓ avol2[n]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ 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 29:
# avol0 = # avol2, # avol1 = # avol2, # lpt1 = # avol2, # buf = EB_PAGE_SIZE, n < # avol2, abs(avol2, bleb0, mkwbuf(buf, m2, m3), avol0, rofs0), awbuf-inv(avol2, bleb0), ebm-vol-inv(avol0), bleb0 ≠ nobuffer → bleb0.leb < # avol2 ∧ wbuf-cons(mkwbuf(buf, m2, m3), avol0[bleb0.leb], rofs0), ∀ m. m < # avol2 → (avol0[m].mapped? → avol1[m] = avol0[m]) ∧ (avol0[m] = unmapped ∧ avol1[m].mapped? → # avol1[m].data ≤ LEB_SIZE ∧ is-aligned(# avol1[m].data, EB_PAGE_SIZE)) ⊦ (avol2[n].mapped? → avol1[n] = mapped(avol2[n].data.align↓)) ∧ (¬ avol2[n].mapped? ∧ avol1[n].mapped? → # avol1[n].data ≤ LEB_SIZE ∧ is-aligned(# avol1[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] → [avol2[n], avol1[n]] flags: <all paths>

Additional information

Used terms: avol2[n], avol1[n]