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Proof step 3 from proof referenced-adrs-lookup-keys-nodups (previous step)

dups(fs[referenced-adrs(ax, ri)].keys), ri-cons(ri, fs) ⊦ dups(ax)

User applied rule structural induction

And obtained the following new goals

Proof step 4:
dups(fs[referenced-adrs(adr + ax0, ri)].keys), ri-cons(ri, fs), ∀ fs, ri. dups(fs[referenced-adrs(ax0, ri)].keys) ∧ ri-cons(ri, fs) → dups(ax0) ⊦ dups(adr + ax0)

Rule argument

indvar: ax

Additional information

Used simplifier rules: referenced-adrs-base: ⊦ referenced-adrs([], ri) = [];%keys-base-01: ⊦ [].keys = [];%address-list freely generated by [], +;;% ⊦ fs[[]] = []; (s)% ⊦ ¬ dups([]); (s)