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Proof step 38 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⊥, n3 < n0 + n, m1 < n0 + n, m1 < # buf + n0, n3 < # buf + n0, m1 < n1, n3 < n1, n3 < n0, afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf ⊦ (m1 ≤ n3 ⊃ zero;getbyte(n3, content0)) = ((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 39:
⊦ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ0[m]
Proof step 40:
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 < n0, n3 < n1, m1 < n1, n3 < # buf + n0, m1 < # buf + n0, m1 < n0 + n, n3 < n0 + n, ⌜n3⌝ < #(content0.stream to n0), afs-cons(dirs, files1), ino ∈ files1, ino ∈ files0, n ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1 ⊦ (m1 ≤ n3 ⊃ zero;getbyte(n3, content0)) = (content0.stream to n0)[n3], n = 0

Rule argument

spec: stream, inst: buffer-inf name: get-append-ls seq: ⊦ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ0[m] subst: [m, σ2, σ0] → [n3, (⌜buf⌝ to n) + (content0.stream from n0 + n), content0.stream to n0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ2[m - (# σ0).n]; (s)% ⊦ # content.stream = ∞; (s)% ⊦ ¬ ∞ < n∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ⌜m⌝ .n = m; (s)%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: n3, (⌜buf⌝ to n) + (content0.stream from n0 + n), content0.stream to n0