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Proof step 6 from proof at-del-ro-nodata (previous step)

key ∈ ri ⊦ (ri \ datakeys(key0, ri))[key] = ri[key], key = key0, key.data?

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: key ∈ datakeys(key0, ri)

Additional information

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