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Proof step 7 from proof del-put-again (previous step)

key ∈ ri[inodekey(m), adr] ⊖ ks ↔ key ∈ ri ⊖ ks, inodekey(m) ∈ ks ⊦ # ks = 0, ks = ∅, (key ∈ ri[inodekey(m), adr] ⊖ ks ↔ key ∈ ri ⊖ ks) ∧ (key ∈ ri[inodekey(m), adr] ⊖ ks → (ri[inodekey(m), adr] ⊖ ks)[key] = (ri ⊖ ks)[key])

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);