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

dups(fs[adr '].keys + fs[referenced-adrs(ax0, ri)].keys), ri-cons(ri, fs), adr ∈ ri ⊦ dups(fs[referenced-adrs(ax0, ri)].keys), dups(ax0), adr ∈ ax0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: keys-one: ⊦ nd '.keys = nd.key ';%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]% ⊦ dups(key ' + kx) ↔ dups(kx) ∨ key ∈ kx; (ws)% ⊦ fs[adr '] = fs[adr] '; (s)