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Proof step 10 from proof del-this (previous step)

key0 = datakey(m, m0), key0.data?, key0 ∈ ri ⊦ (ri[key, adr] ⊖ key)[key0] = (ri ⊖ key)[key0], inodekey(m) = key, key0 = key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
datakey(m, m0) ∈ ri ⊦ (ri[key, adr] ⊖ key)[datakey(m, m0)] = ri[datakey(m, m0)], datakey(m, m0) = key, inodekey(m) = key

Rule argument

Additional information

Used simplifier rules: at-del-ro-data: ⊦ datakey(ino, n) ∈ ri ∧ datakey(ino, n) ≠ key0 ∧ inodekey(ino) ≠ key0 → (ri ⊖ key0)[datakey(ino, n)] = ri[datakey(ino, n)];% ⊦ datakey(m, m0).data?; (s)