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Proof step 6 from proof replay-orphans-data (previous step)

⊦ datakey(ino, n) ∈ ro, inodekey(ino) ∈ 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 weak cut applied rule cut formula

And obtained the following new goals

Proof step 7:
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])
Proof step 13:
⊦ 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])

Rule argument

fma: key = datakey(ino, n)

Additional information

Used formulas: key = datakey(ino, n)