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Proof step 18 from proof inv-evict (previous step)

∀ 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 = datakey(ino0, ino1) ∨ key ∈ evict(ino, pcache0) ⊦ ino = ino0, key.data? ∧ key.ino ≠ ino

User applied rule case distinction

And obtained the following new goals

Proof step 19:
key ∈ evict(ino, pcache0), ∀ 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? ⊦ ino = ino0, key.data? ∧ key.ino ≠ ino

Rule argument

pos: left 3

Additional information

Used simplifier rules: ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).ino = m; (s)