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Proof step 60 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 < m1, afs-cons(dirs, files1), ino ∈ files1, ino ∈ files0, n0 + n ≤ m1, n ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1 ⊦ copy(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 61:
⊦ m0 < # buf → copy(buf0, n, buf, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ buf[m0];buf0[m0 + n - n0])
Proof step 62:
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⊥, n3 < m1, n3 < # (content0.stream to m1).buf, afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf, n0 + n ≤ m1 ⊦ (n3 < n0 ∨ n0 + n ≤ n3 ⊃ (content0.stream to m1).buf[n3];buf[n3 + 0 - n0]) = ((content0.stream to n0) + (⌜buf⌝ to n) + (content0.stream from n0 + n))[n3], n = 0

Rule argument

spec: array-copy, inst: buffer name: at-copy seq: ⊦ m0 < # buf → copy(buf0, n, buf, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ buf[m0];buf0[m0 + n - n0]) subst: [m0, m, n0, buf, n, buf0] → [n3, 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)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: n3, n, n0, (content0.stream to m1).buf, 0, buf