[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 159 from proof inv-write_inode (previous step)

dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), afs-cons(dirs, files), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), synced(dirs, icache, pcache), m ∈ dirs, asynced2 → synced(files, icache, pcache) ⊦ synced(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], icache, pcache), m ∈ icache

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 160:
⊦ synced(dirs, icache, pcache) → (¬ synced(dirs0, icache0, pcache0) ↔ ¬(∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs0 → synced(ino, icache0, pcache0)))
Proof step 161:
dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), afs-cons(dirs, files), synced(dirs, icache, pcache), m ∈ dirs, asynced2 → synced(files, icache, pcache) ⊦ m ∈ icache, ∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)] → synced(ino, icache, pcache)

Rule argument

spec: cache-base name: synced-dirs-variant1 seq: ⊦ synced(dirs, icache, pcache) → ( ¬ synced(dirs0, icache0, pcache0) ↔ ¬ (∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs0 → synced(ino, icache0, pcache0))) subst: [dirs, icache, pcache, dirs0, icache0, pcache0] → [dirs, icache, pcache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], icache, pcache] flags: <all paths>

Additional information

Used terms: dirs, icache, pcache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], icache, pcache