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Proof step 9 from proof refine-write-buf (previous step)

# mkwbuf(buf1, m1, m2).content = EB_PAGE_SIZE, # avol0 = # avol, # lpt0 = # avol, # buf1 = EB_PAGE_SIZE, rofs0 ↔ rofs, avol0[m] = mapped(buf0), wbuf = mkwbuf(buf1, m1, m2), mapped(buf0).mapped?, mkwbuf(buf1, m1, m2).nbytes < # mkwbuf(buf1, m1, m2).content, m < # avol, abs(avol, buffered(m), mkwbuf(buf1, m1, m2), avol0, rofs), awbuf-inv(avol, buffered(m)), ebm-vol-inv(avol0), is-aligned(mkwbuf(buf1, m1, m2).offset, EB_PAGE_SIZE), # avol[m].data + n ≤ LEB_SIZE, n ≤ # buf, ¬ rofs → # mapped(buf0).data = mkwbuf(buf1, m1, m2).offset, rofs → mkwbuf(buf1, m1, m2).offset ≤ # mapped(buf0).data ⊦ ⟪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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# avol0 = # avol, # lpt0 = # avol, # buf1 = EB_PAGE_SIZE, rofs0 ↔ rofs, avol0[m] = mapped(buf0), wbuf = mkwbuf(buf1, m1, m2), m2 < EB_PAGE_SIZE, m < # avol, abs(avol, buffered(m), mkwbuf(buf1, m1, m2), avol0, rofs), awbuf-inv(avol, buffered(m)), ebm-vol-inv(avol0), is-aligned(m1, EB_PAGE_SIZE), # avol[m].data + n ≤ LEB_SIZE, n ≤ # buf, ¬ rofs → # buf0 = m1, rofs → m1 ≤ # buf0 ⊦ ⟪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: ⊦ EB_PAGE_SIZE ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ mkwbuf(buf, m, m0).nbytes = m0; (s)% ⊦ mkwbuf(buf, m, m0).offset = m; (s)% ⊦ mkwbuf(buf, m, m0).content = buf; (s)