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Proof step 49 from proof write-inv-post (previous step)

files1 -- ino = files0 -- ino, (content0.stream from m1)[n4] = zero, files1[ino] = mkfile(m1, md1, # links(ino, dirs), content1), files0[ino] = mkfile(m1, md1, n2, content0), m1 < # buf + n0, m1 < n1, n4 + m1 < n1, n4 + m1 < n0, m1 < n0 + n, m1 < n0, afs-cons(dirs, files1), ino ∈ files0, ino ∈ files1, n0 + n ≤ n1, n1 ≤ # buf + n0, n ≤ # buf ⊦ n = 0, zero = getbyte(n4 + m1, content0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ ⌜n⌝ + ⌜m⌝ < # σ0 → (σ0 from n)[m] = σ0[n + m]

Rule argument

spec: stream, inst: buffer-inf name: get-from seq: ⊦ ⌜n⌝ + ⌜m⌝ < # σ0 → (σ0 from n)[m] = σ0[n + m] subst: [m, n, σ0] → [n4, m1, content0.stream] flags: <all paths>

Additional information

Used simplifier rules: ⊦ content.stream[n] = getbyte(n, content); (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # content.stream = ∞; (s)% ⊦ n∞ < ∞ ↔ n∞ ≠ ∞; (s)% ⊦ ⌜m⌝ + n∞ = ∞ ↔ n∞ = ∞; (s)% ⊦ ⌜m⌝ ≠ ∞; (s)%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf Used terms: n4, m1, content0.stream