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Proof step 7 from proof referenced-adrs-lookup-keys-in-dom (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 8:
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

Rule argument

pos: right 2

Additional information

Used simplifier rules: keys-base-01: ⊦ [].keys = [];% ⊦ fs[[]] = []; (s)% ⊦ [].toSet = ∅; (s)% ⊦ ∅ ⊆ ks; (s)