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Proof step 4 from proof in-del-ro (previous step)

⊦ key ∈ ri \ datakeys(key0, ri) ↔ key ∈ ri ∧ (key.data? → inodekey(key.ino) ≠ key0), key = key0

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: key ∈ ri

Additional information

Used simplifier rules: datakeys: ⊦ key ∈ datakeys(key0, ri) ↔ key ∈ ri ∧ key.data? ∧ key0.inode? ∧ key.ino = key0.ino;% ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ws)% ⊦ inodekey(m).inode?; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ key.inode? → inodekey(key.ino) = key; (s) Used formulas: key ∈ ri