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Proof step 30 from proof write-inv-post (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ # buf < n1 + m ∧ m ≠ 0 → splice(buf0, n0, buf, n1, m) = copy(buf0, n0, resize(buf, n1 + m), n1, m)
Proof step 32:
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⊥, m1 < # buf + n0, n3 < # buf + n0, m1 < n0 + n, n3 < n0 + n, m1 < n1, n3 < n1, # (content0.stream to m1).buf < n0 + n, afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf ⊦ copy(buf, 0, resize((content0.stream to m1).buf, n0 + n), n0, n)[n3] = ((content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n))[n3], n = 0

Rule argument

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

Additional information

Used simplifier rules: ⊦ finp(σ0 to m); (s)%finp(σ) ⊦ # σ.buf = (# σ).n; (s)% ⊦ # content.stream = ∞; (s)% ⊦ ¬ ∞ < n∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ⌜m⌝ .n = m; (s) Used terms: n, n0, (content0.stream to m1).buf, 0, buf