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Proof step 2 from proof put-in (previous step)

⊦ p ∈ ax[a, d] ↔ p = a × d, p ∈ ax

User applied rule structural induction

And obtained the following new goals

Proof step 3:
⊦ a0 × d0 ∈ ax[a, d] ↔ a0 × d0 = a × d, a0 × d0 ∈ ax

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;