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Proof step 4 from proof nuni (previous step)

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

User applied rule structural induction

And obtained the following new goals

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

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;