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Proof step 31 from proof recovery (previous step)

# 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), avol0[n].mapped? → avol1[n] = avol0[n], avol0[n] = unmapped ∧ avol1[n].mapped? → # avol1[n].data ≤ LEB_SIZE ∧ is-aligned(# avol1[n].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))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ abs(avol0, bleb, wbuf, avol1, rofs) ↔ # avol0 = # avol1 ∧ (∀ n. n < # avol0 → (buffered(n) ≠ bleb → avol0[n] = avol1[n]) ∧ (¬ rofs ∧ buffered(n) = bleb → avol0[n] = abs⊕(avol1[n], wbuf)) ∧ ( rofs ∧ buffered(n) = bleb → wbuf.offset = # avol1[n].data ∧ avol0[n] = abs⊕(avol1[n], wbuf) ∨ wbuf.offset < # avol1[n].data ∧ wbuf.offset + wbuf.nbytes < # avol1[n].data ∧ avol0[n] = avol1[n] ∧ subarray(wbuf.content, 0, wbuf.nbytes) = subarray(avol1[n].data, wbuf.offset, wbuf.nbytes)))
Proof step 33:
# buf = EB_PAGE_SIZE, # lpt1 = # avol2, # avol1 = # avol2, # avol0 = # avol2, n < # avol2, awbuf-inv(avol2, bleb0), ebm-vol-inv(avol0), avol0[n] = unmapped ∧ avol1[n].mapped? → # avol1[n].data ≤ LEB_SIZE ∧ is-aligned(# avol1[n].data, EB_PAGE_SIZE), avol0[n].mapped? → avol1[n] = avol0[n], bleb0 ≠ nobuffer → bleb0.leb < # avol2 ∧ wbuf-cons(mkwbuf(buf, m2, m3), avol0[bleb0.leb], rofs0), ∀ n. n < # avol2 → (buffered(n) ≠ bleb0 → avol2[n] = avol0[n]) ∧ (¬ rofs0 ∧ buffered(n) = bleb0 → avol2[n] = abs⊕(avol0[n], mkwbuf(buf, m2, m3))) ∧ ( rofs0 ∧ buffered(n) = bleb0 → mkwbuf(buf, m2, m3).offset = # avol0[n].data ∧ avol2[n] = abs⊕(avol0[n], mkwbuf(buf, m2, m3)) ∨ mkwbuf(buf, m2, m3).offset < # avol0[n].data ∧ mkwbuf(buf, m2, m3).offset + mkwbuf(buf, m2, m3).nbytes < # avol0[n].data ∧ avol2[n] = avol0[n] ∧ subarray(mkwbuf(buf, m2, m3).content, 0, mkwbuf(buf, m2, m3).nbytes) = subarray(avol0[n].data, mkwbuf(buf, m2, m3).offset, mkwbuf(buf, m2, m3).nbytes)) ⊦ (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: wbuf-abs name: abs-def seq: ⊦ abs(avol0, bleb, wbuf, avol1, rofs) ↔ # avol0 = # avol1 ∧ (∀ n. n < # avol0 → (buffered(n) ≠ bleb → avol0[n] = avol1[n]) ∧ ( ¬ rofs ∧ buffered(n) = bleb → avol0[n] = abs⊕(avol1[n], wbuf)) ∧ ( rofs ∧ buffered(n) = bleb → wbuf.offset = # avol1[n].data ∧ avol0[n] = abs⊕(avol1[n], wbuf) ∨ wbuf.offset < # avol1[n].data ∧ wbuf.offset + wbuf.nbytes < # avol1[n].data ∧ avol0[n] = avol1[n] ∧ subarray(wbuf.content, 0, wbuf.nbytes) = subarray (avol1[n].data, wbuf.offset, wbuf.nbytes))) subst: [rofs, avol1, wbuf, bleb, avol0] → [rofs0, avol0, mkwbuf(buf, m2, m3), bleb0, avol2] flags: <all paths>

Additional information

Used terms: rofs0, avol0, mkwbuf(buf, m2, m3), bleb0, avol2