[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 72 from proof abs-nlinks-h (previous step)

tree[p] = dnode(md, sdt), ((m => mkdir(# entries, md, m1, m2, entries) * abs(sdt, entries) * abs|(tree, ino0, p, m)))(dirs), ispath(p, ino0, m, dirs, files), str ∈ sdt, entries[str] ∈ files, ino0 ∈ dirs, p ∈ tree, str ∈ entries, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files ⊦ # links(entries[str], dirs) = 0, ⌜entries[str]⌝ ∈ tree.fids

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 73:
⊦ str ∈ sdt → abs(sdt, sdi) = (⌜str ∈ sdi⌝ ∧ abs(sdt -- str, sdi -- str) * abs(sdt[str], sdi[str]))
Proof step 74:
tree[p] = dnode(md, sdt), (( m => mkdir(# entries, md, m1, m2, entries) * (⌜str ∈ entries⌝ ∧ abs(sdt -- str, entries -- str) * abs(sdt[str], entries[str])) * abs|(tree, ino0, p, m)) )(dirs), ispath(p, ino0, m, dirs, files), str ∈ entries, p ∈ tree, ino0 ∈ dirs, entries[str] ∈ files, str ∈ sdt, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs ⊦ # links(entries[str], dirs) = 0, ⌜entries[str]⌝ ∈ tree.fids

Rule argument

spec: <toplevel> name: entries-recdel seq: ⊦ str ∈ sdt → abs(sdt, sdi) = ( ⌜str ∈ sdi⌝ ∧ abs(sdt -- str, sdi -- str) * abs(sdt[str], sdi[str])) subst: [str, sdi, sdt] → [str, entries, sdt] flags: <all paths>

Additional information

Used terms: str, entries, sdt