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

datakey(ino, n) ∈ ri ⊦ (ri \ datakeys(key0, ri))[datakey(ino, n)] = ri[datakey(ino, n)], datakey(ino, n) = key0, inodekey(ino) = key0

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: datakey(ino, n) ∈ 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)% ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ key.inode? → inodekey(key.ino) = key; (s) Used formulas: datakey(ino, n) ∈ datakeys(key0, ri)