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Proof step 25 from proof refine-unmap (previous step)

# buf = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m] = mapped(buf0), n < # avol1, m4 < # avol1, m < # avol1, abs(avol1, buffered(m), mkwbuf(buf, m3, m2), avol0, rofs), awbuf-inv(avol1, buffered(m)), ebm-vol-inv(avol0), synced(avol1), wbuf-cons(mkwbuf(buf, m3, m2), mapped(buf0), rofs) ⊦ m4 = m, n = m4, (n ≠ m → avol1[n] = avol0[n]) ∧ (¬ rofs ∧ n = m → avol1[m] = mapped(buf0 + subarray(buf, 0, m2))) ∧ ( rofs ∧ n = m → m3 = # buf0 ∧ avol1[m] = mapped(buf0 + subarray(buf, 0, m2)) ∨ m3 < # buf0 ∧ m3 + m2 < # buf0 ∧ avol1[m] = mapped(buf0) ∧ subarray(buf, 0, m2) = subarray(buf0, m3, m2))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ 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 27:
# avol0 = # avol1, # lpt0 = # avol1, # buf = EB_PAGE_SIZE, avol0[m] = mapped(buf0), m < # avol1, m4 < # avol1, n < # avol1, awbuf-inv(avol1, buffered(m)), ebm-vol-inv(avol0), synced(avol1), wbuf-cons(mkwbuf(buf, m3, m2), mapped(buf0), rofs), ∀ n. n < # avol1 → (buffered(n) ≠ buffered(m) → avol1[n] = avol0[n]) ∧ (¬ rofs ∧ buffered(n) = buffered(m) → avol1[n] = abs⊕(avol0[n], mkwbuf(buf, m3, m2))) ∧ ( rofs ∧ buffered(n) = buffered(m) → mkwbuf(buf, m3, m2).offset = # avol0[n].data ∧ avol1[n] = abs⊕(avol0[n], mkwbuf(buf, m3, m2)) ∨ mkwbuf(buf, m3, m2).offset < # avol0[n].data ∧ mkwbuf(buf, m3, m2).offset + mkwbuf(buf, m3, m2).nbytes < # avol0[n].data ∧ avol1[n] = avol0[n] ∧ subarray(mkwbuf(buf, m3, m2).content, 0, mkwbuf(buf, m3, m2).nbytes) = subarray(avol0[n].data, mkwbuf(buf, m3, m2).offset, mkwbuf(buf, m3, m2).nbytes)) ⊦ m4 = m, n = m4, (n ≠ m → avol1[n] = avol0[n]) ∧ (¬ rofs ∧ n = m → avol1[m] = mapped(buf0 + subarray(buf, 0, m2))) ∧ ( rofs ∧ n = m → m3 = # buf0 ∧ avol1[m] = mapped(buf0 + subarray(buf, 0, m2)) ∨ m3 < # buf0 ∧ m3 + m2 < # buf0 ∧ avol1[m] = mapped(buf0) ∧ subarray(buf, 0, m2) = subarray(buf0, m3, m2))

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] → [rofs, avol0, mkwbuf(buf, m3, m2), buffered(m), avol1] flags: <all paths>

Additional information

Used terms: rofs, avol0, mkwbuf(buf, m3, m2), buffered(m), avol1