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

ri-cons(ri, fs), adr ∈ ri, fs[referenced-adrs(ax0, ri)].keys.toSet ⊆ dom ri ⊦ fs[adr].key ∈ fs[referenced-adrs(ax0, ri)].keys, fs[adr '].keys.toSet ⊆ dom ri

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: keys-one: ⊦ nd '.keys = nd.key ';% ⊦ kx.toSet ⊆ dom ri ∧ ¬ key ∈ ri → ¬ key ∈ kx; (s)% ⊦ key ∈ dom ri ↔ key ∈ ri; (s)% ⊦ ∅ ++ key ⊆ ks ↔ key ∈ ks; (s)% ⊦ key '.toSet = ∅ ++ key; (s)% ⊦ fs[adr '] = fs[adr] '; (s)