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Proof step 31 from proof inv-read-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt = # avol, LEB_SIZE = n0 + # buf2, avol[m3] = mapped(buf2), m3 < # avol, EB_PAGE_SIZE < (m0 ≤ m5 ⊃ 0;m0 - m5) + min(n1, n2), ebm-vol-inv(avol), wbuf-cons(mkwbuf(buf1, m5, n2 + (m0 ≤ m5 ⊃ 0;m0 - m5)), mapped(buf2), rofs), (m0 ≤ m5 ⊃ m5 - m0;0) ≤ # buf, m5 ≤ LEB_SIZE, m0 ≤ m5 + n2 + (m0 ≤ m5 ⊃ 0;m0 - m5), m5 ≤ m0 + n1 + (m0 ≤ m5 ⊃ m5 - m0;0), m0 + n1 + (m0 ≤ m5 ⊃ m5 - m0;0) ≤ LEB_SIZE, n1 + (m0 ≤ m5 ⊃ m5 - m0;0) ≤ # buf, # buf2 ≤ LEB_SIZE, (m0 ≤ m5 ⊃ m5 - m0;0) + min(n1, n2) ≤ # buf, ¬ m0 ≤ m5 → m5 ≤ m0 ⊦

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] → [rofs, mapped(buf2), mkwbuf(buf1, m5, n2 + (m0 ≤ m5 ⊃ 0;m0 - m5))] 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)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ m < min(n, m); (s)% ⊦ m +1 = m + 1; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)% ⊦ n ≤ n0 → (m + (n0 - n)) + n = m + n0; (s)% ⊦ m ≤ m + n; (s)%n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s) Used terms: rofs, mapped(buf2), mkwbuf(buf1, m5, n2 + (m0 ≤ m5 ⊃ 0;m0 - m5))