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Proof step 4 from proof nuni (previous step)

unique_al((p ' + ay0) + (a × d)' + az), ∀ a, d, az. a ∈ ay0 ∧ unique_al(ay0 + (a × d)' + az) → a ∈ az, a ∈ p ' ∨ a ∈ ay0 ⊦ a ∈ az

User applied rule structural induction

And obtained the following new goals

Proof step 5:
unique_al(((a0 × d0)' + ay0) + (a × d)' + az), ∀ a, d, az. a ∈ ay0 ∧ unique_al(ay0 + (a × d)' + az) → a ∈ az, a ∈ (a0 × d0)' ∨ a ∈ ay0 ⊦ a ∈ az

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;