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Proof step 5 from proof at-del-ro-nodata (previous step)

key ∈ ri ⊦ ((ri -- key0) \ datakeys(key0, ri))[key] = ri[key], key = key0, key.data?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
key ∈ ri ⊦ (ri \ datakeys(key0, ri))[key] = ri[key], key = key0, key.data?

Rule argument

Additional information

Used simplifier rules: ⊦ key ≠ key0 → (ri -- key0)[key] = ri[key]; (s)% ⊦ (ri -- key) \ ks = (ri \ ks) -- key; (s)