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Proof step 35 from proof refine-remap (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf = EB_PAGE_SIZE, avol0[m] = mapped(buf0), m4 < # avol1, m < # avol1, abs(avol1, buffered(m), mkwbuf(buf, m3, m2), avol0, rofs), awbuf-inv(avol1, buffered(m)), ebm-vol-inv(avol0), synced(avol1), wbuf-cons(mkwbuf(buf, m3, m2), mapped(buf0), rofs) ⊦ m4 = m, # avol1[m4, mapped(mkbuf(0))] = # avol0[m4, mapped(mkbuf(0))] ∧ (∀ n. n < # avol1[m4, mapped(mkbuf(0))] → (buffered(n) ≠ buffered(m) → avol1[m4, mapped(mkbuf(0))][n] = avol0[m4, mapped(mkbuf(0))][n]) ∧ (¬ rofs ∧ buffered(n) = buffered(m) → avol1[m4, mapped(mkbuf(0))][n] = abs⊕(avol0[m4, mapped(mkbuf(0))][n], mkwbuf(buf, m3, m2))) ∧ ( rofs ∧ buffered(n) = buffered(m) → mkwbuf(buf, m3, m2).offset = # avol0[m4, mapped(mkbuf(0))][n].data ∧ avol1[m4, mapped(mkbuf(0))][n] = abs⊕(avol0[m4, mapped(mkbuf(0))][n], mkwbuf(buf, m3, m2)) ∨ mkwbuf(buf, m3, m2).offset < # avol0[m4, mapped(mkbuf(0))][n].data ∧ mkwbuf(buf, m3, m2).offset + mkwbuf(buf, m3, m2).nbytes < # avol0[m4, mapped(mkbuf(0))][n].data ∧ avol1[m4, mapped(mkbuf(0))][n] = avol0[m4, mapped(mkbuf(0))][n] ∧ subarray(mkwbuf(buf, m3, m2).content, 0, mkwbuf(buf, m3, m2).nbytes) = subarray(avol0[m4, mapped(mkbuf(0))][n].data, mkwbuf(buf, m3, m2).offset, mkwbuf(buf, m3, m2).nbytes)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
# avol0 = # avol1, # lpt0 = # avol1, # buf = EB_PAGE_SIZE, avol0[m] = mapped(buf0), n < # avol1, m4 < # avol1, m < # avol1, abs(avol1, buffered(m), mkwbuf(buf, m3, m2), avol0, rofs), awbuf-inv(avol1, buffered(m)), ebm-vol-inv(avol0), synced(avol1), wbuf-cons(mkwbuf(buf, m3, m2), mapped(buf0), rofs) ⊦ m4 = m, (n ≠ m → avol1[m4, mapped(mkbuf(0))][n] = avol0[m4, mapped(mkbuf(0))][n]) ∧ (¬ rofs ∧ n = m → avol1[m] = mapped(buf0 + subarray(buf, 0, m2))) ∧ ( rofs ∧ n = m → m3 = # buf0 ∧ avol1[m] = mapped(buf0 + subarray(buf, 0, m2)) ∨ m3 < # buf0 ∧ m3 + m2 < # buf0 ∧ avol1[m] = mapped(buf0) ∧ subarray(buf, 0, m2) = subarray(buf0, m3, m2))

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)%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)% ⊦ m ≠ n → avol[n, aleb][m] = avol[m]; (s)% ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)% ⊦ abs(avol0, bleb, wbuf, avol1, rofs) → (# avol1 = # avol0 ↔ true); (ss)% ⊦ # avol[n, aleb] = # avol; (s)