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Proof step 112 from proof refine-add-log-leb (previous step)

# buf0 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m] = mapped(buf1), avol0[m5] = mapped(buf), m3 < EB_PAGE_SIZE, m5 < # avol1, m < # avol1, abs(avol1, buffered(m), mkwbuf(buf0, # buf1, m3), avol0, false), awbuf-inv(avol1, buffered(m)), ebm-vol-inv(avol0), is-aligned(# buf1, EB_PAGE_SIZE), synced(avol1) ⊦ m = m5, m3 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 113:
⊦ 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 114:
# avol0 = # avol1, # lpt0 = # avol1, # buf0 = EB_PAGE_SIZE, avol0[m5] = mapped(buf), avol0[m] = mapped(buf1), m < # avol1, m5 < # avol1, m3 < EB_PAGE_SIZE, awbuf-inv(avol1, buffered(m)), ebm-vol-inv(avol0), is-aligned(# buf1, EB_PAGE_SIZE), synced(avol1), ∀ n. n < # avol1 → (buffered(n) ≠ buffered(m) → avol1[n] = avol0[n]) ∧ (¬ false ∧ buffered(n) = buffered(m) → avol1[n] = abs⊕(avol0[n], mkwbuf(buf0, # buf1, m3))) ∧ ( false ∧ buffered(n) = buffered(m) → mkwbuf(buf0, # buf1, m3).offset = # avol0[n].data ∧ avol1[n] = abs⊕(avol0[n], mkwbuf(buf0, # buf1, m3)) ∨ mkwbuf(buf0, # buf1, m3).offset < # avol0[n].data ∧ mkwbuf(buf0, # buf1, m3).offset + mkwbuf(buf0, # buf1, m3).nbytes < # avol0[n].data ∧ avol1[n] = avol0[n] ∧ subarray(mkwbuf(buf0, # buf1, m3).content, 0, mkwbuf(buf0, # buf1, m3).nbytes) = subarray(avol0[n].data, mkwbuf(buf0, # buf1, m3).offset, mkwbuf(buf0, # buf1, m3).nbytes)) ⊦ m = m5, m3 = 0

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, # buf1, m3), buffered(m), avol1] flags: <all paths>

Additional information

Used terms: false, avol0, mkwbuf(buf0, # buf1, m3), buffered(m), avol1