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Proof step 73 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 + n) + n0 < m1, n0 < m1, afs-cons(dirs, files1), ino ∈ files1, ino ∈ files0, n0 + n ≤ m1, n ≤ # buf, n1 ≤ # buf + n0, n0 + n ≤ n1 ⊦ getbyte((n3 + n) + n0, content0) = (content0.stream from n0 + n)[n3], n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

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] → [n3, n0 + n, content0.stream] flags: <all paths>

Additional information

Used simplifier rules: ⊦ content.stream[n] = getbyte(n, content); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf% ⊦ # content.stream = ∞; (s)% ⊦ n∞ < ∞ ↔ n∞ ≠ ∞; (s)% ⊦ ⌜m⌝ + n∞ = ∞ ↔ n∞ = ∞; (s)% ⊦ ⌜m⌝ ≠ ∞; (s)%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf Used terms: n3, n0 + n, content0.stream