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Proof step 24 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 ∧ (n < # avol2 → avol1[n] ↓ avol2[n])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ avol0 ⊆ avol1 ↔ # avol0 = # avol1 ∧ (∀ m. m < # avol0 → (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)))
Proof step 26:
# avol0 = # avol1, # 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), bleb0 ≠ nobuffer → bleb0.leb < # avol2 ∧ wbuf-cons(mkwbuf(buf, m2, m3), avol0[bleb0.leb], rofs0), ∀ m. m < # avol0 → (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 = # avol2 ∧ (n < # avol2 → avol1[n] ↓ avol2[n])

Rule argument

spec: ebm-vol-inv name: ebm-vol-le seq: ⊦ avol0 ⊆ avol1 ↔ # avol0 = # avol1 ∧ (∀ m. m < # avol0 → (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))) subst: [avol1, avol0] → [avol1, avol0] flags: <all paths>

Additional information

Used terms: avol1, avol0