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Proof step 27 from proof write-inv-post (previous step)

files1 -- ino = files0 -- ino, files1[ino] = mkfile(m1, md1, # links(ino, dirs), content1), files0[ino] = mkfile(m1, md1, n2, content0), content0.stream from m1 = σ⊥, afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf ⊦ n = 0, max(m1, n0 + n) = (m1 < n0 + n ⊃ n0 + n;m1) ∧ ( n3 < max(m1, n0 + n) → splice(buf, 0, (content0.stream to m1).buf, n0, n)[n3] = ((content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n))[n3])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: splice-copy seq: ⊦ n1 + m ≤ # buf ∧ m ≠ 0 → splice(buf0, n0, buf, n1, m) = copy(buf0, n0, buf, n1, m) subst: [m, n1, buf, n0, buf0] → [n, n0, (content0.stream to m1).buf, 0, buf] flags: <all paths>

Additional information

Used terms: n, n0, (content0.stream to m1).buf, 0, buf