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Proof step 7 from proof referenced-adrs-lookup-key-cons (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 8:
key-cons(fs[referenced-adrs(ax0, ri)]), ri-cons(ri, fs), adr ∈ ri ⊦ key-cons(fs[adr '])

Rule argument

pos: right 1

Additional information

Used simplifier rules: key-cons-base: ⊦ key-cons([]);% ⊦ fs[[]] = []; (s)