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Proof step 10 from proof lookup-02 (previous step)

a0 ≠ a, unique_al(ax0), a0 × d0 ∈ ax0, ∀ a0, d0. a0 × d0 ∈ ax0 → ax0[a0] = d0 ⊦ a0 × d0 = a × d, ax0[a0] = d0, a ∈ ax0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information