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Proof step 6 from proof inv-evict (previous step)

key ∈ evict(ino, pcache0[key0, pe]), ∀ key. key ∈ pcache0[key0, pe] → key.data?, ∀ key, ino. key ∈ evict(ino, pcache0) ∧ (∀ key. key ∈ pcache0 → key.data?) → key.data? ∧ key.ino ≠ ino ⊦ key.data? ∧ key.ino ≠ ino

User applied rule constructor cut

And obtained the following new goals

Proof step 7:
key0 = inodekey(ino0), key ∈ evict(ino, pcache0[key0, pe]), ∀ key, ino. key ∈ evict(ino, pcache0) ∧ (∀ key. key ∈ pcache0 → key.data?) → key.data? ∧ key.ino ≠ ino, ∀ key. key ∈ pcache0[key0, pe] → key.data? ⊦ key.data? ∧ key.ino ≠ ino
Proof step 9:
key0 = datakey(ino0, ino1), key ∈ evict(ino, pcache0[key0, pe]), ∀ key, ino. key ∈ evict(ino, pcache0) ∧ (∀ key. key ∈ pcache0 → key.data?) → key.data? ∧ key.ino ≠ ino, ∀ key. key ∈ pcache0[key0, pe] → key.data? ⊦ key.data? ∧ key.ino ≠ ino
Proof step 22:
key0 = dentrykey(ino0, name), key ∈ evict(ino, pcache0[key0, pe]), ∀ key, ino. key ∈ evict(ino, pcache0) ∧ (∀ key. key ∈ pcache0 → key.data?) → key.data? ∧ key.ino ≠ ino, ∀ key. key ∈ pcache0[key0, pe] → key.data? ⊦ key.data? ∧ key.ino ≠ ino

Rule argument

var: key0

Additional information

Used simplifier rules: key freely generated by inodekey, datakey, dentrykey;;