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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ (∀ ino0. ino0 ∈ dirs → (ino0 ∈ icache[ino, mkientry(false, inode)] → ¬ icache[ino, mkientry(false, inode)][ino0].dirty) ∧ (∀ n. datakey(ino0, n) ∈ pcache → ¬ pcache[datakey(ino0, n)].dirty)) ↔ (∀ ino0. ino0 ∈ dirs → (ino0 ∈ icache → ¬ icache[ino0].dirty) ∧ (∀ n. datakey(ino0, n) ∈ pcache → ¬ pcache[datakey(ino0, n)].dirty)), ino ∈ icache

Rule argument

Additional information

Used simplifier rules: synced-dirs: ⊦ synced(dirs, icache, pcache) ↔ (∀ ino. ino ∈ dirs → synced(ino, icache, pcache));%synced-ino: ⊦ synced(ino, icache, pcache) ↔ (ino ∈ icache → ¬ icache[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty);