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Proof step 54 from proof truncate-smaller (previous step)

VFS_PAGE_SIZE = n0 + n1, files0[m] = mkfile(m0, md0, # links(m, dirs), content0), n0 ≠ 0, n1 ≠ 0, n1 < VFS_PAGE_SIZE, afs-cons(dirs, files0), m1 ∈ content0, m ∈ files0 ⊦ [asynced := ?] ((content0.stream to m1 * VFS_PAGE_SIZE) + ((content0.stream from m1 * VFS_PAGE_SIZE) to n1) = content0.stream to m1 * VFS_PAGE_SIZE + n1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 55:
⊦ ¬ # σ0 < ⌜n + n1⌝ → (σ0 to n) + ((σ0 from n) to n1) = σ0 to n + n1

Rule argument

spec: stream, inst: buffer-inf name: from-append-tofrom seq: ⊦ ¬ # σ0 < ⌜n + n1⌝ → (σ0 to n) + ((σ0 from n) to n1) = σ0 to n + n1 subst: [n1, n, σ0] → [n1, m1 * VFS_PAGE_SIZE, content0.stream] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # content.stream = ∞; (s)% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ ∞ < n∞; (s)% ⊦ #(content.stream from n) = ∞; (s)% ⊦ ⌜m⌝ < ∞; (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, m1 * VFS_PAGE_SIZE, content0.stream