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Proof step 89 from proof inv-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt = # avol, avol[m4] = mapped(buf2), align↓(m2 + n, EB_PAGE_SIZE) < m2, m4 < # avol, ebm-vol-inv(avol), wbuf-cons(mkwbuf(buf1, m1, m2), mapped(buf2), false), n ≤ # buf, m1 + m2 + n ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n ⊦

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(buf2), mkwbuf(buf1, m1, m2)] flags: <all paths>

Additional information

Used simplifier rules: aligndown-simp: ⊦ m < EB_PAGE_SIZE ∧ EB_PAGE_SIZE ≤ n + m → (align↓(m + n, EB_PAGE_SIZE) < m ↔ false);% ⊦ 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)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≠ 0, m % n = 0 ⊦ align↓(m, n) = m; (s)% ⊦ m +1 = m + 1; (s)% ⊦ m ≤ n → (n < m ↔ false); (s) Used terms: false, mapped(buf2), mkwbuf(buf1, m1, m2)