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Proof step 5 from proof del-this (previous step)

key0 ∈ ri[key, adr] ⊖ key ↔ key0 ∈ ri ⊖ key ⊦ (key0 ∈ ri[key, adr] ⊖ key ↔ key0 ∈ ri ⊖ key) ∧ (key0 ∈ ri[key, adr] ⊖ key → (ri[key, adr] ⊖ key)[key0] = (ri ⊖ key)[key0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: in-del-ro: ⊦ key ∈ ri ⊖ key0 ↔ key ∈ ri ∧ key ≠ key0 ∧ (key.data? → inodekey(key.ino) ≠ key0);% ⊦ key ≠ key0 → (key ∈ ri[key0, adr] ↔ key ∈ ri); (s)