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

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

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: write-inv-others seq: ⊦ write-inv (n0, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1) → (files0 -- ino ≠ files1 -- ino ↔ false) subst: [n0, n1, ino, md, m, m1, m0, buf, n2, dirs, files0, files1] → [m0, n1, m, md, # links(m, dirs), 0, m1, buf, ino, dirs0, files0, files]

Additional information

Used terms: m0, n1, m, md, # links(m, dirs), 0, m1, buf, ino, dirs0, files0, files