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Proof step 62 from proof inv-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt = # avol, avol[m4] = mapped(buf), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, n < m2 + n3, n < # buf3 + m2, m4 < # avol, n < n0 + m2, ebm-vol-inv(avol[m4, mapped(buf + mkempbuf(n1) + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n))]), ebm-vol-inv(avol), is-aligned(n, EB_PAGE_SIZE), is-aligned(n1 + # buf, EB_PAGE_SIZE), wbuf-cons(mkwbuf(buf1, n1 + # buf, m2), mapped(buf), false), EB_PAGE_SIZE ≤ m2 + n3, (n1 + # buf) + m2 + n3 ≤ LEB_SIZE, n3 ≤ # buf3, (n1 + # buf) + n0 + m2 ≤ LEB_SIZE, m2 ≤ EB_PAGE_SIZE, n0 ≤ # buf3, ⌊err0⌋ ⊦ n = 0, wbuf-cons (mkwbuf(buf1, n1 + # buf, m2), mapped(buf + mkempbuf(n1) + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n)), 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 ( buf + mkempbuf(n1) + subarray (copy (buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n)), mkwbuf(buf1, n1 + # buf, 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)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ # subarray(buf, m, n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m + n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ m ≤ m; (s)%⊦ wbuf-cons(mkwbuf(buf, m0, m1), aleb, boolvar) → (EB_PAGE_SIZE ≤ m1 ↔ false); (s)%n ≠ 0, m % n = 0 ⊦ align↓(m, n) = m; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s) Used terms: true, mapped ( buf + mkempbuf(n1) + subarray (copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n)), mkwbuf(buf1, n1 + # buf, m2)