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

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

User applied rule structural induction

And obtained the following new goals

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

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;