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Proof step 20 from proof replay-orphans-data (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
datakey(m, m0) ∈ ri ⊦ ri[datakey(m, m0)] = (ri[datakey(ino, n), adr] ⊖ ro)[datakey(m, m0)], datakey(m, m0) = datakey(ino, n), datakey(ino, n) ∈ ro, inodekey(ino) ∈ ro, datakey(m, m0) ∈ ro, inodekey(m) ∈ ro

Rule argument

Additional information

Used simplifier rules: ⊦ datakey(m, m0).data?; (s)%⊦ datakey(ino, n) ∈ ri ∧ ¬ datakey(ino, n) ∈ ks ∧ ¬ inodekey(ino) ∈ ks → (ri ⊖ ks)[datakey(ino, n)] = ri[datakey(ino, n)]; (s)