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Proof step 2 from proof lookup-02 (previous step)

unique_al(ax), a × d ∈ ax ⊦ ax[a] = d

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ a, d. unique_al(ax0) ∧ a × d ∈ ax0 → ax0[a] = d ⊦ unique_al(p + ax0) ∧ a × d ∈ p + ax0 → (p + ax0)[a] = d

Rule argument

term: ax

Additional information

Used simplifier rules: unique-e: ⊦ unique_al([]);%assoclist freely generated by [], +;;% ⊦ ¬ p ∈ [];