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Proof step 12 from proof inv-evict (previous step)

ino = ino0, key ∈ evict(ino, pcache0[datakey(ino0, ino1), pe]), ∀ key, ino. key ∈ evict(ino, pcache0) ∧ (∀ key. key ∈ pcache0 → key.data?) → key.data? ∧ key.ino ≠ ino, ∀ key. key ∈ pcache0[datakey(ino0, ino1), pe] → key.data? ⊦ key.data? ∧ key.ino ≠ ino

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
key ∈ evict(ino0, pcache0), ∀ key. key ∈ pcache0[datakey(ino0, ino1), pe] → key.data?, ∀ key, ino. key ∈ evict(ino, pcache0) ∧ (∀ key. key ∈ pcache0 → key.data?) → key.data? ∧ key.ino ≠ ino ⊦ key.data? ∧ key.ino ≠ ino0

Rule argument

Additional information

Used simplifier rules: n = ino ⊦ evict(n, pcache[datakey(ino, pageno), pe]) = evict(n, pcache); (s)