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Proof step 1 from proof lookup-02 (conclusion)

⊦ a × d ∈ ax ∧ unique_al(ax) → ax[a] = d

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
unique_al(ax), a × d ∈ ax ⊦ ax[a] = d

Rule argument

Additional information

Used simplifier rules: unique-02: ⊦ unique_al(ax) ∧ a × d ∈ ax ∧ a × d0 ∈ ax → d = d0;