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Proof step 21 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 < m1, afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, n1 ≤ # buf + n0, n0 ≤ n1 ⊦ getbyte(n3, content0) = ((content0.stream to n0) + (content0.stream from n0))[n3], ⌜n3⌝ < #(content0.stream to n0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
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, n0 < m1, afs-cons(dirs, files1), ino ∈ files1, ino ∈ files0, n0 ≤ n1, n1 ≤ # buf + n0, n0 ≤ n3 ⊦ getbyte(n3, content0) = (content0.stream from n0)[n3 - n0]

Rule argument

Additional information

Used simplifier rules: fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]% ⊦ ⌜m⌝ .n = m; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ # content.stream = ∞; (s)% ⊦ ¬ ⌜m⌝ < # σ0 → (σ0 + σ2)[m] = σ2[m - (# σ0).n]; (s)