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

⊦ dentrykey(ino, str) ∈ ro, (key ∈ (ri ⊖ ro)[dentrykey(ino, str), adr] ↔ key ∈ ri[dentrykey(ino, str), adr] ⊖ ro) ∧ (key ∈ (ri ⊖ ro)[dentrykey(ino, str), adr] → (ri ⊖ ro)[dentrykey(ino, str), adr][key] = (ri[dentrykey(ino, str), adr] ⊖ ro)[key])

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 7:
key = dentrykey(ino, str) ⊦ dentrykey(ino, str) ∈ ro, (key ∈ (ri ⊖ ro)[dentrykey(ino, str), adr] ↔ key ∈ ri[dentrykey(ino, str), adr] ⊖ ro) ∧ (key ∈ (ri ⊖ ro)[dentrykey(ino, str), adr] → (ri ⊖ ro)[dentrykey(ino, str), adr][key] = (ri[dentrykey(ino, str), adr] ⊖ ro)[key])
Proof step 13:
⊦ key = dentrykey(ino, str), dentrykey(ino, str) ∈ ro, (key ∈ (ri ⊖ ro)[dentrykey(ino, str), adr] ↔ key ∈ ri[dentrykey(ino, str), adr] ⊖ ro) ∧ (key ∈ (ri ⊖ ro)[dentrykey(ino, str), adr] → (ri ⊖ ro)[dentrykey(ino, str), adr][key] = (ri[dentrykey(ino, str), adr] ⊖ ro)[key])

Rule argument

fma: key = dentrykey(ino, str)

Additional information

Used formulas: key = dentrykey(ino, str)