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Proof step 43 from proof inv-write-buf (previous step)

# lpt = # avol, # buf1 = EB_PAGE_SIZE, avol[m4] = mapped(buf2), m4 < # avol, ebm-vol-inv(avol), ebm-vol-inv (avol [m4, mapped(buf2 + mkempbuf(n0) + copy(buf3, 0, copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), m2, align↓(m2 + n3, EB_PAGE_SIZE) - m2)) ]), is-aligned(n0 + # buf2, EB_PAGE_SIZE), wbuf-cons(mkwbuf(buf1, n0 + # buf2, m2), mapped(buf2), false), (n0 + # buf2) + align↓(m2 + n3, EB_PAGE_SIZE) ≤ LEB_SIZE, (n0 + # buf2) + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, m2 ≤ EB_PAGE_SIZE, align↓(m2 + n3, EB_PAGE_SIZE) ≤ # buf3 + m2, n3 ≤ # buf3, m2 ≤ align↓(m2 + n3, EB_PAGE_SIZE) ⊦ wbuf-cons (mkwbuf (copy(buf3, align↓(m2 + n3, EB_PAGE_SIZE) - m2, buf1, 0, (m2 + n3) % EB_PAGE_SIZE), (n0 + # buf2) + align↓(m2 + n3, EB_PAGE_SIZE), (m2 + n3) % EB_PAGE_SIZE), mapped(buf2 + mkempbuf(n0) + copy(buf3, 0, copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), m2, align↓(m2 + n3, EB_PAGE_SIZE) - m2)), false)

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 + mkempbuf(n0) + copy (buf3, 0, copy (buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), m2, align↓(m2 + n3, EB_PAGE_SIZE) - m2)), mkwbuf (copy (buf3, align↓(m2 + n3, EB_PAGE_SIZE) - m2, buf1, 0, (m2 + n3) % EB_PAGE_SIZE), (n0 + # buf2) + align↓(m2 + n3, EB_PAGE_SIZE), (m2 + n3) % EB_PAGE_SIZE)] 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)% ⊦ # copy(buf, m, buf0, m0, n) = # buf0; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ # mkbuf(n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ mkwbuf(buf, m, m0).offset = m; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ EB_PAGE_SIZE ≠ 0; (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%m ≠ 0 ⊦ is-aligned(align↓(n, m), m); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%n ≠ 0 ⊦ ¬ n ≤ m % n; (s) Used terms: false, mapped ( buf2 + mkempbuf(n0) + copy (buf3, 0, copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), m2, align↓(m2 + n3, EB_PAGE_SIZE) - m2)), mkwbuf (copy (buf3, align↓(m2 + n3, EB_PAGE_SIZE) - m2, buf1, 0, (m2 + n3) % EB_PAGE_SIZE), (n0 + # buf2) + align↓(m2 + n3, EB_PAGE_SIZE), (m2 + n3) % EB_PAGE_SIZE)