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Proof step 29 from proof inv-commit (previous step)

# buf = EB_PAGE_SIZE, # lpt0 = # avol, # lpt = # avol, avol[m] = mapped(buf0), m < # avol, ebm-vol-inv(avol), wbuf-cons(mkwbuf(buf, m1, m2), mapped(buf0), rofs), ⌊err0⌋ ⊦ wbuf-cons(mkwbuf(buf, m1, m2), mapped(buf0), true)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ 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 31:
# mkwbuf(buf, m1, m2).content = EB_PAGE_SIZE, # lpt = # avol, # lpt0 = # avol, # buf = EB_PAGE_SIZE, avol[m] = mapped(buf0), mapped(buf0).mapped?, mkwbuf(buf, m1, m2).nbytes < # mkwbuf(buf, m1, m2).content, m < # avol, ebm-vol-inv(avol), is-aligned(mkwbuf(buf, m1, m2).offset, EB_PAGE_SIZE), ⌊err0⌋ , ¬ rofs → # mapped(buf0).data = mkwbuf(buf, m1, m2).offset, rofs → mkwbuf(buf, m1, m2).offset ≤ # mapped(buf0).data ⊦ wbuf-cons(mkwbuf(buf, m1, m2), mapped(buf0), true)

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(buf, m1, m2)] flags: <all paths>

Additional information

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