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Proof step 5 from proof at-evict-other (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 6:
key = inodekey(ino1), datakey(ino, pageno) ∈ pcache0, ∀ ino, pageno, ino0. datakey(ino, pageno) ∈ pcache0 → evict(ino0, pcache0)[datakey(ino, pageno)] = pcache0[datakey(ino, pageno)] ∨ ino = ino0 ⊦ evict(ino0, pcache0[key, pe])[datakey(ino, pageno)] = pcache0[datakey(ino, pageno)], datakey(ino, pageno) = key, ino = ino0
Proof step 8:
key = datakey(ino1, ino2), datakey(ino, pageno) ∈ pcache0, ∀ ino, pageno, ino0. datakey(ino, pageno) ∈ pcache0 → evict(ino0, pcache0)[datakey(ino, pageno)] = pcache0[datakey(ino, pageno)] ∨ ino = ino0 ⊦ evict(ino0, pcache0[key, pe])[datakey(ino, pageno)] = pcache0[datakey(ino, pageno)], datakey(ino, pageno) = key, ino = ino0
Proof step 15:
key = dentrykey(ino1, name), datakey(ino, pageno) ∈ pcache0, ∀ ino, pageno, ino0. datakey(ino, pageno) ∈ pcache0 → evict(ino0, pcache0)[datakey(ino, pageno)] = pcache0[datakey(ino, pageno)] ∨ ino = ino0 ⊦ evict(ino0, pcache0[key, pe])[datakey(ino, pageno)] = pcache0[datakey(ino, pageno)], datakey(ino, pageno) = key, ino = ino0

Rule argument

var: key

Additional information

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