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Proof step 3 from proof read-write-other (previous step)

⊦ ri[key, adr][kx] = ri[kx], key ∈ kx

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 4:
∀ ri, key, adr. ri[key, adr][kx0] = ri[kx0] ∨ key ∈ kx0 ⊦ ri[key, adr][key0 + kx0] = ri[key0 + kx0], key ∈ key0 + kx0

Rule argument

term: kx

Additional information

Used simplifier rules: index-lookup-base: ⊦ ri[[]] = [];%key-list freely generated by [], +;;