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

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

User applied rule case distinction

And obtained the following new goals

Proof step 8:
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

Rule argument

pos: left 1

Additional information

Used simplifier rules: keys-base-01: ⊦ [].keys = [];% ⊦ fs[[]] = []; (s)% ⊦ [] + kx = kx; (s)%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]