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Proof step 21 from proof synced-files-update-clean-inode (previous step)

icache[ino] = mkientry(false, inode0), pcache[datakey(ino, n)] = mkpentry(true, buf), datakey(ino, n) ∈ pcache, ino ∈ icache, ino ∈ files, ∀ ino0. ino0 ∈ files → (ino0 ∈ icache → ¬ icache[ino0].dirty) ∧ (∀ n. datakey(ino0, n) ∈ pcache → ¬ pcache[datakey(ino0, n)].dirty) ⊦

User applied rule all left

And obtained the following new goals

Proof step 22:
pcache[datakey(ino, n)] = mkpentry(true, buf), icache[ino] = mkientry(false, inode0), ino ∈ files, ino ∈ icache, datakey(ino, n) ∈ pcache, ino ∈ files → (ino ∈ icache → ¬ icache[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty), ∀ ino0. ino0 ∈ files → (ino0 ∈ icache → ¬ icache[ino0].dirty) ∧ (∀ n. datakey(ino0, n) ∈ pcache → ¬ pcache[datakey(ino0, n)].dirty) ⊦

Rule argument

pos: left 6 terms: ino abort: F discard: F computed: T

Additional information

Used terms: ino