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Proof step 108 from proof truncate-empty (previous step)

files0[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), afs-cons(dirs, files0), ino0 ∈ files0 ⊦ [asynced := ?] ((content0.stream to m0 * VFS_PAGE_SIZE) + σ⊥ from m0 * VFS_PAGE_SIZE = σ⊥)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: stream, inst: buffer-inf name: append-from-ge-02 seq: ⊦ ¬ ⌜m⌝ < # σ1 → σ1 + σ2 from m = σ2 from (m - (# σ1).n) subst: [m, σ2, σ1] → [m0 * VFS_PAGE_SIZE, σ⊥, content0.stream to m0 * VFS_PAGE_SIZE] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # content.stream = ∞; (s)% ⊦ ¬ ∞ < n∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ m; (s)% ⊦ ⌜m⌝ .n = m; (s)% ⊦ m - m = 0; (s)% ⊦ σ⊥ from n = σ⊥; (s)% ⊦ ¬ n < n; (s)% ⊦ ⌜m⌝ < ∞; (s)% ⊦ #(σ0 + σ2) = # σ0 + # σ2; (s)% ⊦ # σ⊥ = ∞; (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%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]% ⊦ ⌜0⌝ < n∞ ↔ n∞ ≠ ⌜0⌝ ; (s)% ⊦ ⌜m⌝ ≠ ∞; (s)% ⊦ n ≥ m ↔ m ≤ n; (s) Used terms: m0 * VFS_PAGE_SIZE, σ⊥, content0.stream to m0 * VFS_PAGE_SIZE