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Proof step 11 from proof abs-files-evict (previous step)

⊦ inodekey(ino0) ∈ ri, (ino0 = ino ∨ ¬ inodekey(ino0) ∈ ri \ datakeys(inodekey(ino), ri) ∨ fs[(∅)[inodekey(ino0)]].directory) ∧ ( ino0 ≠ ino ∧ inodekey(ino0) ∈ ri \ datakeys(inodekey(ino), ri) ∧ ¬ fs[(∅)[inodekey(ino0)]].directory → abs-files(fs, ri \ datakeys(inodekey(ino), ri))[ino0] = abs-files(fs, ri)[ino0])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store+set, inst: node-index name: Diff-ext seq: ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks subst: [ks, ri, key] → [datakeys(inodekey(ino), ri), ri, inodekey(ino0)] flags: <all paths>

Additional information

Used terms: datakeys(inodekey(ino), ri), ri, inodekey(ino0)