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Proof step 7 from proof refine-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt0 = # avol, # avol0 = # avol, rofs0 ↔ rofs, avol0[m] = mapped(buf0), wbuf = mkwbuf(buf1, m1, m2), m < # avol, abs(avol, buffered(m), mkwbuf(buf1, m1, m2), avol0, rofs), awbuf-inv(avol, buffered(m)), ebm-vol-inv(avol0), wbuf-cons(mkwbuf(buf1, m1, m2), 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ wbuf-cons(wbuf, aleb, rofs) ↔ aleb.mapped? ∧ wbuf.nbytes < # wbuf.content ∧ # wbuf.content = EB_PAGE_SIZE ∧ (¬ rofs → # aleb.data = wbuf.offset) ∧ (rofs → wbuf.offset ≤ # aleb.data) ∧ is-aligned(wbuf.offset, EB_PAGE_SIZE)
Proof step 9:
# 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)

Rule argument

spec: wbuf-base name: wbuf-cons seq: ⊦ wbuf-cons(wbuf, aleb, rofs) ↔ aleb.mapped? ∧ wbuf.nbytes < # wbuf.content ∧ # wbuf.content = EB_PAGE_SIZE ∧ (¬ rofs → # aleb.data = wbuf.offset) ∧ (rofs → wbuf.offset ≤ # aleb.data) ∧ is-aligned(wbuf.offset, EB_PAGE_SIZE) subst: [rofs, aleb, wbuf] → [rofs, mapped(buf0), mkwbuf(buf1, m1, m2)] flags: <all paths>

Additional information

Used terms: rofs, mapped(buf0), mkwbuf(buf1, m1, m2)