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Proof step 7 from proof replay-orphans-data (previous step)

key = datakey(ino, n) ⊦ inodekey(ino) ∈ ro, datakey(ino, n) ∈ ro, (key ∈ (ri ⊖ ro)[datakey(ino, n), adr] ↔ key ∈ ri[datakey(ino, n), adr] ⊖ ro) ∧ (key ∈ (ri ⊖ ro)[datakey(ino, n), adr] → (ri ⊖ ro)[datakey(ino, n), adr][key] = (ri[datakey(ino, n), adr] ⊖ ro)[key])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
⊦ datakey(ino, n) ∈ ro, inodekey(ino) ∈ ro, datakey(ino, n) ∈ ri[datakey(ino, n), adr] ⊖ ro ∧ adr = (ri[datakey(ino, n), adr] ⊖ ro)[datakey(ino, n)]

Rule argument

Additional information

Used simplifier rules: ⊦ ri[key, adr][key] = adr; (s)% ⊦ key ∈ ri[key, adr]; (s)