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Proof step 9 from proof abs-dirs-deldatakeys-2 (previous step)

fs[ri[inodekey(ino)]].directory, inodekey(ino) ∈ ri ⊦ (dentrykey(ino, str) ∈ ri \ datakeys(key, n, ri) → dentrykey(ino, str) ∈ ri) ∧ (dentrykey(ino, str) ∈ ri \ datakeys(key, n, ri) → fs[(ri \ datakeys(key, n, ri))[dentrykey(ino, str)]].ino = fs[ri[dentrykey(ino, str)]].ino)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Rule argument

fma: dentrykey(ino, str) ∈ ri

Additional information

Used simplifier rules: ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ws) Used formulas: dentrykey(ino, str) ∈ ri