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Proof step 315 from proof refine-read-buf (previous step)

# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, LEB_SIZE = n0 + # buf4, LEB_SIZE = n1 + # buf1, avol0[n2] = mapped(buf), avol0[m2] = mapped(buf4), avol1[m2] = mapped(buf1), n2 < # avol1, m2 < # avol1, m4 < EB_PAGE_SIZE, abs(avol1, buffered(n2), mkwbuf(buf2, m6, m4), avol0, rofs), awbuf-inv(avol1, buffered(n2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), m0 + n ≤ LEB_SIZE, # buf4 ≤ LEB_SIZE, n ≤ # buf3, # buf1 ≤ LEB_SIZE, rofs → m6 ≤ # buf, ¬ rofs → # buf = m6 ⊦ copy(buf4 + mkempbuf(n0), m0, buf3, 0, n) = copy(buf1 + mkempbuf(n1), m0, buf3, 0, n), m2 = n2 ∧ m0 ≤ m6 + m4 ∧ m6 ≤ m0 + n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 316:
⊦ 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 317:
# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + # buf1, LEB_SIZE = n0 + # buf4, avol1[m2] = mapped(buf1), avol0[m2] = mapped(buf4), avol0[n2] = mapped(buf), m4 < EB_PAGE_SIZE, m2 < # avol1, n2 < # avol1, awbuf-inv(avol1, buffered(n2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), # buf1 ≤ LEB_SIZE, n ≤ # buf3, # buf4 ≤ LEB_SIZE, m0 + n ≤ LEB_SIZE, ¬ rofs → # buf = m6, rofs → m6 ≤ # buf, ∀ n. n < # avol1 → (buffered(n) ≠ buffered(n2) → avol1[n] = avol0[n]) ∧ (¬ rofs ∧ buffered(n) = buffered(n2) → avol1[n] = abs⊕(avol0[n], mkwbuf(buf2, m6, m4))) ∧ ( rofs ∧ buffered(n) = buffered(n2) → mkwbuf(buf2, m6, m4).offset = # avol0[n].data ∧ avol1[n] = abs⊕(avol0[n], mkwbuf(buf2, m6, m4)) ∨ mkwbuf(buf2, m6, m4).offset < # avol0[n].data ∧ mkwbuf(buf2, m6, m4).offset + mkwbuf(buf2, m6, m4).nbytes < # avol0[n].data ∧ avol1[n] = avol0[n] ∧ subarray(mkwbuf(buf2, m6, m4).content, 0, mkwbuf(buf2, m6, m4).nbytes) = subarray(avol0[n].data, mkwbuf(buf2, m6, m4).offset, mkwbuf(buf2, m6, m4).nbytes)) ⊦ copy(buf4 + mkempbuf(n0), m0, buf3, 0, n) = copy(buf1 + mkempbuf(n1), m0, buf3, 0, n), m2 = n2 ∧ m0 ≤ m6 + m4 ∧ m6 ≤ m0 + n

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(buf2, m6, m4), buffered(n2), avol1] flags: <all paths>

Additional information

Used terms: rofs, avol0, mkwbuf(buf2, m6, m4), buffered(n2), avol1