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Proof step 75 from proof refine-commit (previous step)

# lpt2 = # avol1, # avol0 = # avol1, # lpt1 = # avol1, # buf = EB_PAGE_SIZE, avol0[m] = mapped(buf0), m < # avol1, abs(avol1, buffered(m), mkwbuf(buf, m1, m2), avol0, rofs), awbuf-inv(avol1, buffered(m)), ebm-vol-inv(avol0), synced(avol1), wbuf-cons(mkwbuf(buf, m1, m2), mapped(buf0), rofs), ⌊err1⌋ ⊦ # avol1 = # avol0 ∧ (∀ n. n < # avol1 → (buffered(n) ≠ buffered(m) → avol1[n] = avol0[n]) ∧ (¬ true ∧ buffered(n) = buffered(m) → avol1[n] = abs⊕(avol0[n], mkwbuf(buf, m1, m2))) ∧ ( true ∧ buffered(n) = buffered(m) → mkwbuf(buf, m1, m2).offset = # avol0[n].data ∧ avol1[n] = abs⊕(avol0[n], mkwbuf(buf, m1, m2)) ∨ mkwbuf(buf, m1, m2).offset < # avol0[n].data ∧ mkwbuf(buf, m1, m2).offset + mkwbuf(buf, m1, m2).nbytes < # avol0[n].data ∧ avol1[n] = avol0[n] ∧ subarray(mkwbuf(buf, m1, m2).content, 0, mkwbuf(buf, m1, m2).nbytes) = subarray(avol0[n].data, mkwbuf(buf, m1, m2).offset, mkwbuf(buf, m1, m2).nbytes)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 76:
# lpt2 = # avol1, # avol0 = # avol1, # lpt1 = # avol1, # buf = EB_PAGE_SIZE, avol0[m] = mapped(buf0), n < # avol1, m < # avol1, abs(avol1, buffered(m), mkwbuf(buf, m1, m2), avol0, rofs), awbuf-inv(avol1, buffered(m)), ebm-vol-inv(avol0), synced(avol1), wbuf-cons(mkwbuf(buf, m1, m2), mapped(buf0), rofs), ⌊err1⌋ ⊦ (n ≠ m → avol1[n] = avol0[n]) ∧ ( n = m → m1 = # buf0 ∧ avol1[m] = mapped(buf0 + subarray(buf, 0, m2)) ∨ m1 < # buf0 ∧ m1 + m2 < # buf0 ∧ avol1[m] = mapped(buf0) ∧ subarray(buf, 0, m2) = subarray(buf0, m1, m2))

Rule argument

Additional information

Used simplifier rules: ⊦ abs⊕(mapped(buf), wbuf) = mapped(buf + subarray(wbuf.content, 0, wbuf.nbytes)); (s)% ⊦ mapped(buf).data = buf; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ mkwbuf(buf, m, m0).content = buf; (s)% ⊦ mkwbuf(buf, m, m0).nbytes = m0; (s)% ⊦ mkwbuf(buf, m, m0).offset = m; (s)% ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)