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Proof step 8 from proof del-this (previous step)

key0 ∈ ri, key0.data? → inodekey(key0.ino) ≠ key ⊦ (ri[key, adr] ⊖ key)[key0] = (ri ⊖ key)[key0], key0 = key, key0 ∈ ri[key, adr] ∧ key0 ≠ key ∧ ¬ key0.data?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
key0.data?, key0 ∈ ri ⊦ (ri[key, adr] ⊖ key)[key0] = (ri ⊖ key)[key0], inodekey(key0.ino) = key, key0 = key

Rule argument

Additional information

Used simplifier rules: ⊦ key ≠ key0 → (key ∈ ri[key0, adr] ↔ key ∈ ri); (s)