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Proof step 4 from proof refine-write-buf (previous step)

# wbuf.content = EB_PAGE_SIZE, # lpt0 = # avol, # avol0 = # avol, rofs0 ↔ rofs, avol0[m] = mapped(buf0), bleb0 = buffered(m), m < # avol, abs(avol, bleb0, wbuf, avol0, rofs), awbuf-inv(avol, bleb0), ebm-vol-inv(avol0), wbuf-cons(wbuf, mapped(buf0), rofs), n ≤ # buf, # avol[m].data + n ≤ LEB_SIZE ⊦ ⟪wbuf_write_buf#(n, buf, bleb0, EB_PAGE_SIZE, adr0, m0, plog0, lpt0, ns0; wbuf, rofs, avol0; err)⟫ ⟨awbuf_write_buf#(n, buf, adr0, m0, plog0, lpt0, ns0, bleb0; avol, rofs0; err0)⟩ (abs(avol, bleb0, wbuf, avol0, rofs) ∧ (rofs0 ↔ rofs) ∧ err = err0), bleb0 = nobuffer

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
# wbuf.content = EB_PAGE_SIZE, # lpt0 = # avol, # avol0 = # avol, rofs0 ↔ rofs, avol0[m] = mapped(buf0), m < # avol, abs(avol, buffered(m), wbuf, avol0, rofs), awbuf-inv(avol, buffered(m)), ebm-vol-inv(avol0), wbuf-cons(wbuf, mapped(buf0), rofs), n ≤ # buf, # avol[m].data + n ≤ LEB_SIZE ⊦ ⟪wbuf_write_buf#(n, buf, buffered(m), EB_PAGE_SIZE, adr0, m0, plog0, lpt0, ns0; wbuf, rofs, avol0; err)⟫ ⟨awbuf_write_buf#(n, buf, adr0, m0, plog0, lpt0, ns0, buffered(m); avol, rofs0; err0)⟩ (abs(avol, buffered(m), wbuf, avol0, rofs) ∧ (rofs0 ↔ rofs) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ nobuffer ≠ buffered(m); (s)