[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 71 from proof truncate-inv (previous step)

files2[ino4] = mkfile(m2 * VFS_PAGE_SIZE, md, # links(ino4, dirs0), content2), afs-cons(dirs0, files2), afs-cons(dirs0, files2[ino4, mkfile(m2 * VFS_PAGE_SIZE, md, # links(ino4, dirs0), content2 upto m2 * VFS_PAGE_SIZE)]), files2 ~ files2[ino4, mkfile(m2 * VFS_PAGE_SIZE, md, # links(ino4, dirs0), content2 upto m2 * VFS_PAGE_SIZE)], ino4 ∈ files2 ⊦ (content2.stream to m2 * VFS_PAGE_SIZE) + σ⊥ from m2 * 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] → [m2 * VFS_PAGE_SIZE, σ⊥, content2.stream to m2 * 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; (s)% ⊦ m - m = 0; (s)% ⊦ σ⊥ from n = σ⊥; (s)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)% ⊦ m0 * m < m0 * n ↔ m0 ≠ 0 ∧ m < n; (ws)% ⊦ ¬ n < n; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: m2 * VFS_PAGE_SIZE, σ⊥, content2.stream to m2 * VFS_PAGE_SIZE