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Proof step 17 from proof refine-enter-readonly (previous step)

# 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# 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), ∀ n0. n0 < # avol → (n0 ≠ m → avol[n0] = avol0[n0]) ∧ (¬ rofs ∧ n0 = m → avol[m] = mapped(buf0 + subarray(buf, 0, m1))) ∧ ( rofs ∧ n0 = 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)) ⊦ (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: ⊦ mapped(buf).data = buf; (s)%⊦ abs⊕(mapped(buf), wbuf) = mapped(buf + subarray(wbuf.content, 0, wbuf.nbytes)); (s)% ⊦ 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)