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Proof step 32 from proof inv-commit (previous step)

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

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

Additional information

Used simplifier rules: ⊦ mapped(buf).mapped?; (s)% ⊦ mkwbuf(buf, m, m0).nbytes = m0; (s)% ⊦ mkwbuf(buf, m, m0).content = buf; (s)% ⊦ mkwbuf(buf, m, m0).offset = m; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m < n → ¬ n < m; (s) Used terms: true, mapped(buf0), mkwbuf(buf, m1, m2)