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Proof step 37 from proof refine-destroy-buf (previous step)

# buf = EB_PAGE_SIZE, # lpt0 = # avol, # avol0 = # avol, avol0[m] = mapped(buf0), avol[m] = mapped(buf0 + subarray(buf, 0, m1)), m < # avol, awbuf-inv(avol, buffered(m)), ebm-vol-inv(avol0), is-aligned(# buf0 + m1, EB_PAGE_SIZE), wbuf-cons(mkwbuf(buf, m2, m1), mapped(buf0), false), ∀ n0. n0 < # avol → n0 ≠ m → avol[n0] = avol0[n0] ⊦ m1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

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] → [false, mapped(buf0), mkwbuf(buf, m2, m1)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mkwbuf(buf, m, m0).content = buf; (s)% ⊦ mkwbuf(buf, m, m0).offset = m; (s)% ⊦ mkwbuf(buf, m, m0).nbytes = m0; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%m ≠ 0 ⊦ is-aligned(n, m) → (n < m ↔ n = 0); (s) Used terms: false, mapped(buf0), mkwbuf(buf, m2, m1)