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Proof step 25 from proof readpage-prepost (previous step)

# buf = VFS_PAGE_SIZE, files[m0] = mkfile(n0, md, # links(m0, dirs), content), n1 < VFS_PAGE_SIZE, F(files -- m0), afs-cons(dirs, files), n ∈ content, m0 ∈ files ⊦ content[n][n1] = (content.stream from n * VFS_PAGE_SIZE)[n1]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ ⌜n⌝ + ⌜m⌝ < # σ0 → (σ0 from n)[m] = σ0[n + m]
Proof step 27:
# buf = VFS_PAGE_SIZE, files[m0] = mkfile(n0, md, # links(m0, dirs), content), n1 < VFS_PAGE_SIZE, ⌜n * VFS_PAGE_SIZE⌝ + ⌜n1⌝ < # content.stream, F(files -- m0), afs-cons(dirs, files), m0 ∈ files, n ∈ content ⊦ content[n][n1] = content.stream[n * VFS_PAGE_SIZE + n1]

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] → [n1, n * VFS_PAGE_SIZE, content.stream] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # 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: n1, n * VFS_PAGE_SIZE, content.stream