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Proof step 24 from proof read-inv-post (previous step)

# buf0 = # buf1, buf1[n2] = (content.stream from n0)[n2], files[ino] = mkfile(m, md, # links(ino, dirs), content), ⌜# buf1⌝ = ⌜n⌝ + #(⌜buf0⌝ from n), n2 < n, n2 < # buf1, afs-cons(dirs, files), ino ∈ files, n ≤ # buf1, n1 ≤ # buf1 + n0, n0 + n ≤ m, n0 + n ≤ n1 ⊦ getbyte(n2 + n0, content) = buf1[n2]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ ⌜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] → [n2, n0, content.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: n2, n0, content.stream