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Proof step 111 from proof truncate-empty (previous step)

files0[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n0 ≠ 0, n0 < VFS_PAGE_SIZE, afs-cons(dirs, files0), ino0 ∈ files0, ¬ m0 ∈ content0 ⊦ [asynced := ?] (((content0.stream to VFS_PAGE_SIZE * m0) + (σ⊥ to VFS_PAGE_SIZE)) + σ⊥ from m0 * VFS_PAGE_SIZE + n0 = σ⊥)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 112:
⊦ ¬ # σ1 < ⌜n⌝ ∧ ¬ # σ2 < ⌜n1⌝ → (σ1 to n) + σ2 from n1 + n = σ2 from n1
Proof step 113:
files0[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n0 < VFS_PAGE_SIZE, afs-cons(dirs, files0), ino0 ∈ files0 ⊦ [asynced := ?] ((σ⊥ to VFS_PAGE_SIZE) + σ⊥ from n0 = σ⊥), n0 = 0, #((σ⊥ to VFS_PAGE_SIZE) + σ⊥) < ⌜n0⌝ , # content0.stream < ⌜VFS_PAGE_SIZE * m0⌝ , m0 ∈ content0

Rule argument

spec: stream, inst: buffer-inf name: from-append-add seq: ⊦ ¬ # σ1 < ⌜n⌝ ∧ ¬ # σ2 < ⌜n1⌝ → (σ1 to n) + σ2 from n1 + n = σ2 from n1 subst: [n1, σ2, n, σ1] → [n0, (σ⊥ to VFS_PAGE_SIZE) + σ⊥, VFS_PAGE_SIZE * m0, content0.stream] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # content.stream = ∞; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ #(σ0 + σ2) = # σ0 + # σ2; (s)% ⊦ # σ⊥ = ∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to 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% ⊦ ⌜m⌝ < ∞; (s)% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n∞ < ∞ ↔ n∞ ≠ ∞; (s)% ⊦ ⌜m⌝ + n∞ = ∞ ↔ n∞ = ∞; (s)% ⊦ ⌜m⌝ ≠ ∞; (s)%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]%mult-c: ⊦ m * n = n * m; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic Used terms: n0, (σ⊥ to VFS_PAGE_SIZE) + σ⊥, VFS_PAGE_SIZE * m0, content0.stream