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Proof step 14 from proof refine-enter-readonly (previous step)

# avol0 = # avol, # lpt0 = # avol, # buf = EB_PAGE_SIZE, avol0[m] = mapped(buf0), 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) ⊦ # avol = # avol0 ∧ (∀ n. n < # avol → (buffered(n) ≠ buffered(m) → avol[n] = avol0[n]) ∧ (¬ true ∧ buffered(n) = buffered(m) → avol[n] = abs⊕(avol0[n], mkwbuf(buf, m2, m1))) ∧ ( true ∧ 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)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
# 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))

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)