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Proof step 15 from proof refine-enter-readonly (previous step)

# avol0 = # avol, # lpt0 = # avol, # buf = EB_PAGE_SIZE, avol0[m] = mapped(buf0), n < # avol, m < # avol, abs(avol, buffered(m), mkwbuf(buf, m2, m1), avol0, rofs), awbuf-inv(avol, buffered(m)), ebm-vol-inv(avol0), wbuf-cons(mkwbuf(buf, m2, m1), mapped(buf0), rofs) ⊦ (n ≠ m → avol[n] = avol0[n]) ∧ ( n = m → m2 = # buf0 ∧ avol[m] = mapped(buf0 + subarray(buf, 0, m1)) ∨ m2 < # buf0 ∧ m2 + m1 < # buf0 ∧ avol[m] = mapped(buf0) ∧ subarray(buf, 0, m1) = subarray(buf0, m2, m1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ 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 17:
# buf = EB_PAGE_SIZE, # lpt0 = # avol, # avol0 = # avol, avol0[m] = mapped(buf0), m < # avol, n < # avol, awbuf-inv(avol, buffered(m)), ebm-vol-inv(avol0), wbuf-cons(mkwbuf(buf, m2, m1), mapped(buf0), rofs), ∀ n. n < # avol → (buffered(n) ≠ buffered(m) → avol[n] = avol0[n]) ∧ (¬ rofs ∧ buffered(n) = buffered(m) → avol[n] = abs⊕(avol0[n], mkwbuf(buf, m2, m1))) ∧ ( rofs ∧ buffered(n) = buffered(m) → mkwbuf(buf, m2, m1).offset = # avol0[n].data ∧ avol[n] = abs⊕(avol0[n], mkwbuf(buf, m2, m1)) ∨ mkwbuf(buf, m2, m1).offset < # avol0[n].data ∧ mkwbuf(buf, m2, m1).offset + mkwbuf(buf, m2, m1).nbytes < # avol0[n].data ∧ avol[n] = avol0[n] ∧ subarray(mkwbuf(buf, m2, m1).content, 0, mkwbuf(buf, m2, m1).nbytes) = subarray(avol0[n].data, mkwbuf(buf, m2, m1).offset, mkwbuf(buf, m2, m1).nbytes)) ⊦ (n ≠ m → avol[n] = avol0[n]) ∧ ( n = m → m2 = # buf0 ∧ avol[m] = mapped(buf0 + subarray(buf, 0, m1)) ∨ m2 < # buf0 ∧ m2 + m1 < # buf0 ∧ avol[m] = mapped(buf0) ∧ subarray(buf, 0, m1) = subarray(buf0, m2, m1))

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(buf, m2, m1), buffered(m), avol] flags: <all paths>

Additional information

Used terms: rofs, avol0, mkwbuf(buf, m2, m1), buffered(m), avol