[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 59 from proof inv-evict (previous step)

# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, entries), afs-cons(dirs, files), afs-cons(dirs -- m, files), synced(dirs, icache, pcache), m ∈ dirs, asynced1 → synced(files, icache, pcache) ⊦ m = ROOT_INO, synced(dirs -- m, icache -- m, pcache)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 60:
⊦ synced(dirs, icache, pcache) → (¬ synced(dirs0, icache0, pcache0) ↔ ¬(∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs0 → synced(ino, icache0, pcache0)))
Proof step 61:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, entries), afs-cons(dirs -- m, files), afs-cons(dirs, files), synced(dirs, icache, pcache), m ∈ dirs, asynced1 → synced(files, icache, pcache) ⊦ m = ROOT_INO, ∀ ino. (ino ∈ dirs → synced(ino, icache, pcache)) → ino ∈ dirs -- m → synced(ino, icache -- m, 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, icache -- m, pcache] flags: <all paths>

Additional information

Used terms: dirs, icache, pcache, dirs -- m, icache -- m, pcache