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Proof step 42 from proof refine-move-buf (previous step)

# buf = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m5] = mapped(buf0), m5 < # avol1, abs(avol1, bleb0, mkwbuf(buf, m4, m3), avol0, false), awbuf-inv(avol1, bleb0), ebm-vol-inv(avol0), bleb0 ≠ nobuffer → avol1[bleb0.leb].mapped? ∧ bleb0.leb < # avol1 ∧ bleb0.isbuf?, bleb0 ≠ nobuffer → bleb0.leb < # avol1 ∧ wbuf-cons(mkwbuf(buf, m4, m3), avol0[bleb0.leb], false), bleb0 = nobuffer ∨ m3 = 0, bleb0 = nobuffer ∨ is-aligned(# avol1[bleb0.leb].data, EB_PAGE_SIZE) ⊦ bleb0 = buffered(m5), abs(avol1, buffered(m5), mkwbuf(buf, # buf0, 0), avol0, false)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 43:
⊦ 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 44:
# avol0 = # avol1, # lpt0 = # avol1, # buf = EB_PAGE_SIZE, avol0[m5] = mapped(buf0), m5 < # avol1, abs(avol1, bleb0, mkwbuf(buf, m4, m3), avol0, false), awbuf-inv(avol1, bleb0), ebm-vol-inv(avol0), bleb0 ≠ nobuffer → bleb0.leb < # avol1 ∧ wbuf-cons(mkwbuf(buf, m4, m3), avol0[bleb0.leb], false), bleb0 ≠ nobuffer → avol1[bleb0.leb].mapped? ∧ bleb0.leb < # avol1 ∧ bleb0.isbuf?, bleb0 = nobuffer ∨ is-aligned(# avol1[bleb0.leb].data, EB_PAGE_SIZE), bleb0 = nobuffer ∨ m3 = 0 ⊦ bleb0 = 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(buf, # buf0, 0))) ∧ ( false ∧ buffered(n) = buffered(m5) → mkwbuf(buf, # buf0, 0).offset = # avol0[n].data ∧ avol1[n] = abs⊕(avol0[n], mkwbuf(buf, # buf0, 0)) ∨ mkwbuf(buf, # buf0, 0).offset < # avol0[n].data ∧ mkwbuf(buf, # buf0, 0).offset + mkwbuf(buf, # buf0, 0).nbytes < # avol0[n].data ∧ avol1[n] = avol0[n] ∧ subarray(mkwbuf(buf, # buf0, 0).content, 0, mkwbuf(buf, # buf0, 0).nbytes) = subarray(avol0[n].data, mkwbuf(buf, # buf0, 0).offset, mkwbuf(buf, # buf0, 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(buf, # buf0, 0), buffered(m5), avol1] flags: <all paths>

Additional information

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