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Proof step 70 from proof inv-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt = # avol, avol[m4] = mapped(buf), m4 < # avol, ebm-vol-inv(avol), is-aligned(m3, EB_PAGE_SIZE), wbuf-cons(mkwbuf(buf1, m3, m2), mapped(buf), false), EB_PAGE_SIZE ≤ m2 + n3, m2 ≤ EB_PAGE_SIZE, align↓(m2 + n3, EB_PAGE_SIZE) ≤ # buf3 + m2, m3 + m2 + n3 ≤ LEB_SIZE, n3 ≤ # buf3, # buf ≤ m3, m3 + align↓(m2 + n3, EB_PAGE_SIZE) ≤ LEB_SIZE, m2 ≤ align↓(m2 + n3, EB_PAGE_SIZE), ⌊err0⌋ ⊦ wbuf-cons(mkwbuf(buf1, m3, m2), mapped(buf), true)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 71:
⊦ 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 72:
# lpt = # avol, # buf1 = EB_PAGE_SIZE, avol[m4] = mapped(buf), m4 < # avol, ebm-vol-inv(avol), is-aligned(m3, EB_PAGE_SIZE), wbuf-cons(mkwbuf(buf1, m3, m2), mapped(buf), false), m2 ≤ align↓(m2 + n3, EB_PAGE_SIZE), m3 + align↓(m2 + n3, EB_PAGE_SIZE) ≤ LEB_SIZE, # buf ≤ m3, n3 ≤ # buf3, m3 + m2 + n3 ≤ LEB_SIZE, align↓(m2 + n3, EB_PAGE_SIZE) ≤ # buf3 + m2, m2 ≤ EB_PAGE_SIZE, EB_PAGE_SIZE ≤ m2 + n3, ⌊err0⌋ ⊦ mapped(buf).mapped? ∧ mkwbuf(buf1, m3, m2).nbytes < # mkwbuf(buf1, m3, m2).content ∧ # mkwbuf(buf1, m3, m2).content = EB_PAGE_SIZE ∧ (¬ true → # mapped(buf).data = mkwbuf(buf1, m3, m2).offset) ∧ (true → mkwbuf(buf1, m3, m2).offset ≤ # mapped(buf).data) ∧ is-aligned(mkwbuf(buf1, m3, m2).offset, EB_PAGE_SIZE)

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] → [true, mapped(buf), mkwbuf(buf1, m3, m2)] flags: <all paths>

Additional information

Used terms: true, mapped(buf), mkwbuf(buf1, m3, m2)