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Proof step 3 from proof keys-at (previous step)

n < # ax ⊦ keys(fs, ax)[n] = fs[ax[n]].key, ax = []

User applied rule structural induction

And obtained the following new goals

Proof step 4:
n < #(adr + ax0), ∀ n, fs. n < # ax0 → keys(fs, ax0)[n] = fs[ax0[n]].key ∨ ax0 = [] ⊦ adr + ax0 = [], keys(fs, adr + ax0)[n] = fs[(adr + ax0)[n]].key

Rule argument

indvar: ax

Additional information

Used simplifier rules: address-list freely generated by [], +;;