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

datakey(ino, pageno) ∈ pcache0[key, pe], ∀ 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[key, pe][datakey(ino, pageno)], ino = ino0

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 4:
datakey(ino, pageno) ∈ pcache0[key, pe], ∀ 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[key, pe][datakey(ino, pageno)], datakey(ino, pageno) = key, ino = ino0

Rule argument

fma: datakey(ino, pageno) = key

Additional information

Used simplifier rules: evict-rec-other: n ≠ ino ⊦ evict(n, pcache[datakey(ino, pageno), pe]) = evict(n, pcache)[datakey(ino, pageno), pe];% ⊦ pcache[key, pe][key] = pe; (s) Used formulas: datakey(ino, pageno) = key