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Proof step 10 from proof abs-files-evict (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
⊦ 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])

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ key ∈ ri → ri[key] = (∅)[key]; (s)