[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 9 from proof inv-rename-dentry (previous step)

new_child_inode.ino = dirs[m].entries[str], old_child_inode.ino = dirs[old_parent_inode.ino].entries[str0], old_parent_inode.nlink = dirs[old_parent_inode.ino].nlink, old_parent_inode.nsubdirs = dirs[old_parent_inode.ino].nsubdirs, old_parent_inode.size = dirs[old_parent_inode.ino].size, new_child_inode.ino ∈ files ↔ old_child_inode.ino ∈ files, new_dent = mkdentry(str, new_child_inode.ino), new_parent_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), old_dent = mkdentry(str0, old_child_inode.ino), old_parent_inode.directory, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str ∈ dirs[m].entries, str0 ∈ dirs[old_parent_inode.ino].entries, m ∈ dirs, old_parent_inode.ino ∈ dirs, new_child_inode.ino ∈ dirs → new_child_inode.ino ≠ ROOT_INO ∧ dirs[new_child_inode.ino].entries = ∅, m = old_parent_inode.ino → md = old_parent_inode.meta, asynced → synced(files, icache, pcache), new_child_inode.ino ∈ dirs ∨ old_child_inode.ino ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, old_child_inode.ino ∈ dirs ∨ old_child_inode.ino ∈ files, links(old_parent_inode.ino, dirs) ≠ ∅ ∨ old_parent_inode.ino = ROOT_INO, new_child_inode.ino ∈ dirs ∧ new_child_inode.nlink = dirs[new_child_inode.ino].nlink ∧ new_child_inode.size = dirs[new_child_inode.ino].size ∧ new_child_inode.nsubdirs = dirs[new_child_inode.ino].nsubdirs ∧ new_child_inode.directory ∨ old_child_inode.ino ∈ files ∧ new_child_inode.nlink = files[new_child_inode.ino].nlink ∧ new_child_inode.nsubdirs = 0 ∧ ¬ new_child_inode.directory, old_child_inode.ino ∈ dirs ∧ old_child_inode.nlink = dirs[old_child_inode.ino].nlink ∧ old_child_inode.size = dirs[old_child_inode.ino].size ∧ old_child_inode.nsubdirs = dirs[old_child_inode.ino].nsubdirs ∧ old_child_inode.directory ∨ old_child_inode.ino ∈ files ∧ old_child_inode.nlink = files[old_child_inode.ino].nlink ∧ old_child_inode.nsubdirs = 0 ∧ ¬ old_child_inode.directory ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
old_child_inode.ino = dirs[m0].entries[str0], new_child_inode.ino = dirs[m].entries[str], new_child_inode.ino ∈ files ↔ old_child_inode.ino ∈ files, boolvar, m1 = dirs[m0].nlink, m2 = dirs[m0].nsubdirs, m3 = dirs[m0].size, new_dent = mkdentry(str, new_child_inode.ino), new_parent_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), old_dent = mkdentry(str0, old_child_inode.ino), old_parent_inode = mkinode(m0, md0, boolvar, m1, m2, m3), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m0 ∈ dirs, m ∈ dirs, str0 ∈ dirs[m0].entries, str ∈ dirs[m].entries, asynced → synced(files, icache, pcache), m = m0 → md = md0, new_child_inode.ino ∈ dirs → new_child_inode.ino ≠ ROOT_INO ∧ dirs[new_child_inode.ino].entries = ∅, old_child_inode.ino ∈ dirs ∧ old_child_inode.nlink = dirs[old_child_inode.ino].nlink ∧ old_child_inode.size = dirs[old_child_inode.ino].size ∧ old_child_inode.nsubdirs = dirs[old_child_inode.ino].nsubdirs ∧ old_child_inode.directory ∨ old_child_inode.ino ∈ files ∧ old_child_inode.nlink = files[old_child_inode.ino].nlink ∧ old_child_inode.nsubdirs = 0 ∧ ¬ old_child_inode.directory, new_child_inode.ino ∈ dirs ∧ new_child_inode.nlink = dirs[new_child_inode.ino].nlink ∧ new_child_inode.size = dirs[new_child_inode.ino].size ∧ new_child_inode.nsubdirs = dirs[new_child_inode.ino].nsubdirs ∧ new_child_inode.directory ∨ old_child_inode.ino ∈ files ∧ new_child_inode.nlink = files[new_child_inode.ino].nlink ∧ new_child_inode.nsubdirs = 0 ∧ ¬ new_child_inode.directory, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, old_child_inode.ino ∈ dirs ∨ old_child_inode.ino ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, new_child_inode.ino ∈ dirs ∨ old_child_inode.ino ∈ files ⊦ ⟪cache_rename# (; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [old_parent_inode, m0, md0, boolvar, m1, m2, m3]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: old_parent_inode, m0, md0, boolvar, m1, m2, m3