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Proof step 21 from proof read-inv-post (previous step)

# buf0 = # buf1, buf1[n3 + n] = (⌜buf0⌝ from n)[n3], files[ino] = mkfile(m, md, # links(ino, dirs), content), ⌜# buf1⌝ = ⌜n⌝ + #(⌜buf0⌝ from n), n < # buf1, n3 + n < # buf1, afs-cons(dirs, files), ino ∈ files, n1 ≤ # buf1 + n0, n0 + n ≤ m, n0 + n ≤ n1 ⊦ buf0[n3 + n] = buf1[n3 + n]

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, n, ⌜buf0⌝ ] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # ⌜buf⌝ = ⌜# buf⌝ ; (s)% ⊦ ⌜n⌝ + ⌜m⌝ < ⌜n0⌝ ↔ n + m < n0; (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%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n < # buf → ⌜buf⌝ [n] = buf[n]; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ ¬ n < n; (s) Used terms: n3, n, ⌜buf0⌝