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Proof step 3 from proof in-evict-other (previous step)

∀ ino, pageno, ino0. (datakey(ino, pageno) ∈ evict(ino0, pcache0) ↔ datakey(ino, pageno) ∈ pcache0) ∨ ino = ino0 ⊦ datakey(ino, pageno) ∈ evict(ino0, pcache0[key, pe]) ↔ datakey(ino, pageno) ∈ pcache0[key, pe], ino = ino0

User applied rule constructor cut

And obtained the following new goals

Proof step 4:
key = inodekey(ino1), ∀ ino, pageno, ino0. (datakey(ino, pageno) ∈ evict(ino0, pcache0) ↔ datakey(ino, pageno) ∈ pcache0) ∨ ino = ino0 ⊦ datakey(ino, pageno) ∈ evict(ino0, pcache0[key, pe]) ↔ datakey(ino, pageno) ∈ pcache0[key, pe], ino = ino0
Proof step 6:
key = datakey(ino1, ino2), ∀ ino, pageno, ino0. (datakey(ino, pageno) ∈ evict(ino0, pcache0) ↔ datakey(ino, pageno) ∈ pcache0) ∨ ino = ino0 ⊦ datakey(ino, pageno) ∈ evict(ino0, pcache0[key, pe]) ↔ datakey(ino, pageno) ∈ pcache0[key, pe], ino = ino0
Proof step 18:
key = dentrykey(ino1, name), ∀ ino, pageno, ino0. (datakey(ino, pageno) ∈ evict(ino0, pcache0) ↔ datakey(ino, pageno) ∈ pcache0) ∨ ino = ino0 ⊦ datakey(ino, pageno) ∈ evict(ino0, pcache0[key, pe]) ↔ datakey(ino, pageno) ∈ pcache0[key, pe], ino = ino0

Rule argument

var: key

Additional information

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