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

ri[fs[referenced-adrs(ax0, ri)].keys] = referenced-adrs(ax0, ri), ri-cons(ri, fs), adr ∈ ri ⊦ ri[fs[adr '].keys] = (adr ∈ ri ⊃ adr ';[])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: keys-one: ⊦ nd '.keys = nd.key ';% ⊦ adr ' = adr0 ' ↔ adr = adr0; (s)% ⊦ ri[key '] = ri[key] '; (s)% ⊦ fs[adr '] = fs[adr] '; (s)