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Proof step 8 from proof referenced-adrs-lookup-key-cons (previous step)

key-cons(fs[referenced-adrs(ax0, ri)]), ri-cons(ri, fs), adr ∈ ri ⊦ key-cons(fs[adr '])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
key-cons(fs[referenced-adrs(ax0, ri)]), ri-cons(ri, fs), adr ∈ ri ⊦ key-cons(fs[adr].key, fs[adr])

Rule argument

Additional information

Used simplifier rules: key-cons-one: ⊦ key-cons(nd ') ↔ key-cons(nd.key, nd);% ⊦ fs[adr '] = fs[adr] '; (s)