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Proof step 2 from proof synced-files-add-new-clean-inode (previous step)

⊦ synced(files, icache[ino, mkientry(false, inode)], pcache) ↔ synced(files, icache, pcache), ino ∈ icache

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ synced(files, icache, pcache) ↔ (∀ ino. ino ∈ files → synced(ino, icache, pcache))
Proof step 4:
⊦ synced(files, icache[ino, mkientry(false, inode)], pcache) ↔ (∀ ino. ino ∈ files → synced(ino, icache, pcache)), ino ∈ icache

Rule argument

spec: <toplevel> name: synced-files seq: ⊦ synced(files, icache, pcache) ↔ (∀ ino. ino ∈ files → synced(ino, icache, pcache)) subst: [pcache, icache, files] → [pcache, icache, files] flags: <all paths>

Additional information

Used terms: pcache, icache, files