[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 116 from proof truncate-empty (previous step)

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⊥ ∧ (∀ n. ⌜n⌝ < #((σ⊥ to VFS_PAGE_SIZE) + σ⊥ from n0) → ((σ⊥ to VFS_PAGE_SIZE) + σ⊥ from n0)[n] = (σ⊥)[n])), n0 = 0, m0 ∈ content0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 117:
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))

Rule argument

Additional information

Used simplifier rules: ⊦ (σ⊥)[n] = zero; (s)% ⊦ ⌜m⌝ ≠ ∞; (s)% ⊦ ⌜m⌝ + n∞ = ∞ ↔ n∞ = ∞; (s)% ⊦ n∞ < ∞ ↔ n∞ ≠ ∞; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)%⌜n⌝ < # σ0 ⊦ ⌜n0⌝ < #(σ0 from n) ↔ ⌜n0 + n⌝ < # σ0; (s)% ⊦ ⌜m⌝ < ∞; (s)%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf% ⊦ ⌜m⌝ + ∞ = ∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ #(σ0 + σ2) = # σ0 + # σ2; (s)% ⊦ # σ⊥ = ∞; (s)