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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
datakey(ino, n) ∈ ri ⊦ (ri \ datakeys(key0, ri))[datakey(ino, n)] = ri[datakey(ino, n)], datakey(ino, n) = key0, inodekey(ino) = key0

Rule argument

Additional information

Used simplifier rules: ⊦ key ≠ key0 → (ri -- key0)[key] = ri[key]; (s)% ⊦ (ri -- key) \ ks = (ri \ ks) -- key; (s)