[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 60 from proof truncate-empty (previous step)

VFS_PAGE_SIZE = n0 + n1, files1[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), m0 ∈ content0, ino0 ∈ files1, m0 * VFS_PAGE_SIZE + n1 ≤ VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE ⊦ [asynced := ?] ( ( ( (content0.stream to m0 * VFS_PAGE_SIZE + n1) + (σ⊥ to n0) + (content0.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) from m0 * VFS_PAGE_SIZE + n1) to (VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE - m0 * VFS_PAGE_SIZE + n1)) + σ⊥ = σ⊥), n0 = 0, n1 = 0, #((content0.stream to m0 * VFS_PAGE_SIZE + n1) + (σ⊥ to n0) + (content0.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE)) < ⌜VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 61:
VFS_PAGE_SIZE = n0 + n1, files1[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), n0 ≠ 0, n1 ≠ 0, n1 < VFS_PAGE_SIZE, afs-cons(dirs, files1), ino0 ∈ files1, m0 ∈ content0 ⊦ [asynced := ?] ( ( ( (content0.stream to m0 * VFS_PAGE_SIZE + n1) + (σ⊥ to n0) + (content0.stream from VFS_PAGE_SIZE * m0 + VFS_PAGE_SIZE) from m0 * VFS_PAGE_SIZE + n1) to (VFS_PAGE_SIZE - n1)) + σ⊥ = σ⊥)

Rule argument

Additional information

Used simplifier rules: ⊦ m + n - n + n1 = m - n1; (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)% ⊦ #(content.stream from n) = ∞; (s)% ⊦ # σ⊥ = ∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)% ⊦ # content.stream = ∞; (s)% ⊦ #(σ0 + σ2) = # σ0 + # σ2; (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)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult