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Proof step 4 from proof insnotin (previous step)

∀ a, d. ax0[a, d] = ax0 + (a × d)' ∨ a ∈ ax0 ⊦ (p ' + ax0)[a, d] = (p ' + ax0) + (a × d)', a ∈ p ', a ∈ ax0

User applied rule structural induction

And obtained the following new goals

Proof step 5:
∀ a, d. ax0[a, d] = ax0 + (a × d)' ∨ a ∈ ax0 ⊦ ((a0 × d0)' + ax0)[a, d] = ((a0 × d0)' + ax0) + (a × d)', a ∈ (a0 × d0)', a ∈ ax0

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;