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Proof step 35 from proof inv-recover (previous step)

afs-cons(dirs0, files1), pcache-cons(pcache1, dirs0, files1), synced(dirs0, icache1, pcache1), asynced4 → synced(files1, icache1, pcache1) ⊦ pcache-cons(∅, dirs0 \ orphans(dirs0, files1), files1 \ orphans(dirs0, files1))

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ pcache-cons(pcache, dirs, files) ↔ (∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part]))

Rule argument

spec: cache-base name: pcache-cons seq: ⊦ pcache-cons(pcache, dirs, files) ↔ (∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ ( ¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part])) subst: [pcache, dirs, files] → [∅, dirs0 \ orphans(dirs0, files1), files1 \ orphans(dirs0, files1)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ key ∈ ∅; (s) Used terms: ∅, dirs0 \ orphans(dirs0, files1), files1 \ orphans(dirs0, files1)