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Proof step 59 from proof refine-add-log-leb (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf0 = EB_PAGE_SIZE, avol0[m5] = mapped(buf), m5 < # avol1, abs(avol1, bleb, mkwbuf(buf0, m4, m3), avol0, false), awbuf-inv(avol1, bleb), ebm-vol-inv(avol0), synced(avol1), bleb ≠ nobuffer → bleb.leb < # avol1 ∧ wbuf-cons(mkwbuf(buf0, m4, m3), avol0[bleb.leb], false), bleb = nobuffer ∨ m3 = 0 ⊦ bleb = buffered(m5), abs(avol1, buffered(m5), mkwbuf(buf0, # buf, 0), avol0, false)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 60:
⊦ 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 61:
# buf0 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m5] = mapped(buf), m5 < # avol1, abs(avol1, bleb, mkwbuf(buf0, m4, m3), avol0, false), awbuf-inv(avol1, bleb), ebm-vol-inv(avol0), synced(avol1), bleb ≠ nobuffer → bleb.leb < # avol1 ∧ wbuf-cons(mkwbuf(buf0, m4, m3), avol0[bleb.leb], false), bleb = nobuffer ∨ m3 = 0 ⊦ bleb = buffered(m5), # avol1 = # avol0 ∧ (∀ n. n < # avol1 → (buffered(n) ≠ buffered(m5) → avol1[n] = avol0[n]) ∧ (¬ false ∧ buffered(n) = buffered(m5) → avol1[n] = abs⊕(avol0[n], mkwbuf(buf0, # buf, 0))) ∧ ( false ∧ buffered(n) = buffered(m5) → mkwbuf(buf0, # buf, 0).offset = # avol0[n].data ∧ avol1[n] = abs⊕(avol0[n], mkwbuf(buf0, # buf, 0)) ∨ mkwbuf(buf0, # buf, 0).offset < # avol0[n].data ∧ mkwbuf(buf0, # buf, 0).offset + mkwbuf(buf0, # buf, 0).nbytes < # avol0[n].data ∧ avol1[n] = avol0[n] ∧ subarray(mkwbuf(buf0, # buf, 0).content, 0, mkwbuf(buf0, # buf, 0).nbytes) = subarray(avol0[n].data, mkwbuf(buf0, # buf, 0).offset, mkwbuf(buf0, # buf, 0).nbytes)))

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(buf0, # buf, 0), buffered(m5), avol1] flags: <all paths>

Additional information

Used terms: false, avol0, mkwbuf(buf0, # buf, 0), buffered(m5), avol1