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

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

User applied rule structural induction

And obtained the following new goals

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

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)% ⊦ ri[[]] = []; (s)