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

⟨afs_truncate#(n0 + m0, (n0 + m0) / VFS_PAGE_SIZE; buf-opt, inode1, isdir, err, dirs1, files1, asynced1)⟩ ( buf-opt = buf-opt0 ∧ inode1 = mkinode(m, md, false, m3, 0, n0 + m0) ∧ (isdir ↔ isdir0) ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced1 ↔ asynced0)), # links(m, dirs1) = m3, files1 -- m = files0 -- m, files[m] = mkfile(n0 + m0, md, # links(m, dirs1), content1), files0[m] = mkfile(n0 + m0, md, # links(m, dirs1), content), of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(n0 + m0, md, # links(m, dirs1), content0), buf-opt = none, err = ESUCCESS, content.stream from n0 + m0 = σ⊥, inode1 = mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), content0.stream to n0 + m0 = content.stream to n0 + m0, n1 ≠ 0, n1 < ino, n0 < ino, n1 < n0, n1 + 1 < ino, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), buf, ino, dirs0, files0, files), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, n0 + m0), buf, 0, dirs0, files0, files0), files1 ~ files0, fd ∈ of1, m ∈ files1, m ∈ files, n1 ≤ # buf, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: write-inv-ls seq: ⊦ write-inv (n0, n0 + n1, mkinode(ino, md, false, m, m1, m0), buf, n2, dirs, files0, files1) → n2 ≤ n1 subst: [n0, n1, ino, md, m, m1, m0, buf, n2, dirs, files0, files1] → [m0, n1, m, md, # links(m, dirs1), 0, n0 + m0, buf, ino, dirs0, files0, files]

Additional information

Used simplifier rules: ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: m0, n1, m, md, # links(m, dirs1), 0, n0 + m0, buf, ino, dirs0, files0, files