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Proof step 7 from proof unique-add (previous step)

unique_al(p ' + ax0), unique_al(ax0), ∀ a, d. a ∈ ax0 ∨ unique_al(ax0 + (a × d)') ⊦ a ∈ p ', a ∈ ax0, unique_al((p ' + ax0) + (a × d)')

User applied rule structural induction

And obtained the following new goals

Proof step 8:
unique_al((a0 × d0)' + ax0), unique_al(ax0), ∀ a, d. a ∈ ax0 ∨ unique_al(ax0 + (a × d)') ⊦ a ∈ (a0 × d0)', a ∈ ax0, unique_al(((a0 × d0)' + ax0) + (a × d)')

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;