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Proof step 10 from proof del-del-again (previous step)

key ∈ ri, inodekey(m) ∈ ks, key.data? → ¬ inodekey(key.ino) ∈ ks, key.data? → key.ino ≠ m ⊦ # ks = 0, ((ri ⊖ ks) ⊖ inodekey(m))[key] = (ri ⊖ ks)[key], ks = ∅, key ∈ ks, key ∈ ri ⊖ ks ∧ key ≠ inodekey(m) ∧ ¬ key.data?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: in-dels-ro: ⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks);