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Proof step 5 from proof at-dels-ro-nodata (previous step)

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

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: key ∈ datakeys(ks, ri)

Additional information

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