[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 252 from proof write-prepost-partial (previous step)

⟨afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err2, dirs1, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err2 = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files0 -- m = files -- m, files1 -- m = files -- m, files[m] = mkfile(m1, md, m3, content1), files0[m] = mkfile(m1, md, # links(m, dirs1), content), files1[m] = mkfile(m1, md, # links(m, dirs1), content0), of1[fd] = mkfile(m, mode, m0), buf-opt = none, err2 = ESUCCESS, content.stream from m1 = σ⊥, inode = mkinode(m, md, false, # links(m, dirs1), 0, m1), inode0 = mkinode(m, md, false, # links(m, dirs1), 0, m1), content0.stream to m1 = content.stream to m1, ((content.stream to m0) + (⌜buf⌝ to ino) + (content.stream from m0 + ino) to m1).buf ≠ (content.stream to m1).buf, ino ≠ 0, n1 ≠ 0, m1 < m0, m1 < m0 + ino, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, m1), buf, ino, dirs0, files0, files), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, m1), buf, 0, dirs0, files0, files0), files1 ~ files0, m ∈ files, m ∈ files1, fd ∈ of1, n1 ≤ # buf, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: stream, inst: buffer-inf name: append-to-ls seq: ⊦ ¬ # σ1 < ⌜n⌝ → σ1 + σ2 to n = σ1 to n subst: [n, σ2, σ1] → [m1, (⌜buf⌝ to ino) + (content.stream from m0 + ino), content.stream to m0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # content.stream = ∞; (s)% ⊦ ¬ ∞ < n∞; (s)%¬ # σ0 < ⌜n⌝ ⊦ m < n → σ0 to n to m = σ0 to m; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)% ⊦ m < n → ¬ n < m; (s) Used terms: m1, (⌜buf⌝ to ino) + (content.stream from m0 + ino), content.stream to m0