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Proof step 117 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 := ?] (#((σ⊥ to VFS_PAGE_SIZE) + σ⊥ from n0) = ∞ ∧ (∀ n. ((σ⊥ to VFS_PAGE_SIZE) + σ⊥ from n0)[n] = zero))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 118:
⊦ # σ0 = ∞ → #(σ0 from n) = ∞
Proof step 119:
#((σ⊥ to VFS_PAGE_SIZE) + σ⊥) = ∞, files0[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n0 < VFS_PAGE_SIZE, afs-cons(dirs, files0), ino0 ∈ files0 ⊦ [asynced := ?] (∞ = ∞ ∧ (∀ n. ((σ⊥ to VFS_PAGE_SIZE) + σ⊥ from n0)[n] = zero)), n0 = 0, m0 ∈ content0

Rule argument

spec: stream, inst: buffer-inf name: inf-size-from seq: ⊦ # σ0 = ∞ → #(σ0 from n) = ∞ subst: [n, σ0] → [n0, (σ⊥ to VFS_PAGE_SIZE) + σ⊥] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(σ0 + σ2) = # σ0 + # σ2; (s)% ⊦ # σ⊥ = ∞; (s)% ⊦ ¬ ∞ < n∞; (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%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]% ⊦ ⌜m⌝ < ∞; (s) Used terms: n0, (σ⊥ to VFS_PAGE_SIZE) + σ⊥