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

datakey(ino, n) ∈ ri ⊦ ((ri \ ks) \ datakeys(ks, ri))[datakey(ino, n)] = ri[datakey(ino, n)], inodekey(ino) ∈ ks, datakey(ino, n) ∈ ks

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: datakey(ino, n) ∈ 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)% ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).ino = m; (s) Used formulas: datakey(ino, n) ∈ datakeys(ks, ri)