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Proof step 204 from proof refine-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, n < # avol1, m4 < # avol1, m2 < EB_PAGE_SIZE, abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, false), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), is-aligned(n0 + m2, EB_PAGE_SIZE), # buf2 + n0 + m2 ≤ LEB_SIZE, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE, n0 ≤ # buf3, ⌊err1⌋ ⊦ n0 + m2 = 0, n3 = 0, (n ≠ m4 → avol1[n] = avol0[n]) ∧ (n = m4 → avol1[m4] = mapped(buf2 + subarray(buf1, 0, m2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 205:
⊦ 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 206:
# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, m2 < EB_PAGE_SIZE, m4 < # avol1, n < # avol1, awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(n0 + m2, EB_PAGE_SIZE), is-aligned(# buf2, EB_PAGE_SIZE), n0 ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE, n3 ≤ # buf3, EB_PAGE_SIZE ≤ m2 + n3, # buf2 + m2 + n3 ≤ LEB_SIZE, # buf2 + n0 + m2 ≤ LEB_SIZE, ⌊err1⌋ , ∀ n. n < # avol1 → (buffered(n) ≠ buffered(m4) → avol1[n] = avol0[n]) ∧ (¬ false ∧ buffered(n) = buffered(m4) → avol1[n] = abs⊕(avol0[n], mkwbuf(buf1, # buf2, m2))) ∧ ( false ∧ buffered(n) = buffered(m4) → mkwbuf(buf1, # buf2, m2).offset = # avol0[n].data ∧ avol1[n] = abs⊕(avol0[n], mkwbuf(buf1, # buf2, m2)) ∨ mkwbuf(buf1, # buf2, m2).offset < # avol0[n].data ∧ mkwbuf(buf1, # buf2, m2).offset + mkwbuf(buf1, # buf2, m2).nbytes < # avol0[n].data ∧ avol1[n] = avol0[n] ∧ subarray(mkwbuf(buf1, # buf2, m2).content, 0, mkwbuf(buf1, # buf2, m2).nbytes) = subarray(avol0[n].data, mkwbuf(buf1, # buf2, m2).offset, mkwbuf(buf1, # buf2, m2).nbytes)) ⊦ n0 + m2 = 0, n3 = 0, (n ≠ m4 → avol1[n] = avol0[n]) ∧ (n = m4 → avol1[m4] = mapped(buf2 + subarray(buf1, 0, 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] → [false, avol0, mkwbuf(buf1, # buf2, m2), buffered(m4), avol1] flags: <all paths>

Additional information

Used terms: false, avol0, mkwbuf(buf1, # buf2, m2), buffered(m4), avol1