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Proof step 61 from proof refine-add-log-leb (previous step)

# buf0 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m5] = mapped(buf), m5 < # avol1, abs(avol1, bleb, mkwbuf(buf0, m4, m3), avol0, false), awbuf-inv(avol1, bleb), ebm-vol-inv(avol0), synced(avol1), bleb ≠ nobuffer → bleb.leb < # avol1 ∧ wbuf-cons(mkwbuf(buf0, m4, m3), avol0[bleb.leb], false), bleb = nobuffer ∨ m3 = 0 ⊦ bleb = buffered(m5), # avol1 = # avol0 ∧ (∀ n. n < # avol1 → (buffered(n) ≠ buffered(m5) → avol1[n] = avol0[n]) ∧ (¬ false ∧ buffered(n) = buffered(m5) → avol1[n] = abs⊕(avol0[n], mkwbuf(buf0, # buf, 0))) ∧ ( false ∧ buffered(n) = buffered(m5) → mkwbuf(buf0, # buf, 0).offset = # avol0[n].data ∧ avol1[n] = abs⊕(avol0[n], mkwbuf(buf0, # buf, 0)) ∨ mkwbuf(buf0, # buf, 0).offset < # avol0[n].data ∧ mkwbuf(buf0, # buf, 0).offset + mkwbuf(buf0, # buf, 0).nbytes < # avol0[n].data ∧ avol1[n] = avol0[n] ∧ subarray(mkwbuf(buf0, # buf, 0).content, 0, mkwbuf(buf0, # buf, 0).nbytes) = subarray(avol0[n].data, mkwbuf(buf0, # buf, 0).offset, mkwbuf(buf0, # buf, 0).nbytes)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 62:
# buf0 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m5] = mapped(buf), n < # avol1, m5 < # avol1, abs(avol1, bleb, mkwbuf(buf0, m4, m3), avol0, false), awbuf-inv(avol1, bleb), ebm-vol-inv(avol0), synced(avol1), bleb ≠ nobuffer → bleb.leb < # avol1 ∧ wbuf-cons(mkwbuf(buf0, m4, m3), avol0[bleb.leb], false), bleb = nobuffer ∨ m3 = 0 ⊦ avol1[n] = avol0[n], bleb = buffered(m5), n = m5

Rule argument

Additional information

Used simplifier rules: abs-unbuffered: n < # avol0 ⊦ abs(avol0, bleb, wbuf, avol1, rofs) ∧ avol1[n] = mapped(buf) ∧ bleb ≠ buffered(n) → avol0[n] = mapped(buf);% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ buf + mkbuf(0) = buf; (s)% ⊦ subarray(buf, n, 0) = mkbuf(0); (s)% ⊦ mkwbuf(buf, m, m0).nbytes = m0; (s)% ⊦ mkwbuf(buf, m, m0).content = 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% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)