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Proof step 4 from proof unique-01 (previous step)

unique_al((p ' + ax0) + (a × d)'), unique_al(p ' + ax0), a ∈ p ' ∨ a ∈ ax0, ∀ a0, d0. ¬ a0 ∈ ax0 ∨ ¬ unique_al(ax0 + (a0 × d0)') ∨ ¬ unique_al(ax0) ⊦

User applied rule structural induction

And obtained the following new goals

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

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;