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Proof step 2 from proof in-evict-other (previous step)

⊦ datakey(ino, pageno) ∈ evict(ino0, pcache) ↔ datakey(ino, pageno) ∈ pcache, ino = ino0

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ 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

indvar: pcache

Additional information

Used simplifier rules: evict-base: ⊦ evict(n, ∅) = ∅;%pcache generated by ∅, [ ];;% ⊦ ¬ key ∈ ∅; (s)