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Proof step 4 from proof unique-02 (previous step)

unique_al(p ' + ax0), ∀ a, d0, d. a × d0 ∈ ax0 ∧ a × d ∈ ax0 ∧ unique_al(ax0) → d = d0 ⊦ d = d0, ¬ a × d0 ∈ ax0 ∧ a × d0 ≠ p, ¬ a × d ∈ ax0 ∧ a × d ≠ p

User applied rule structural induction

And obtained the following new goals

Proof step 5:
⊦ unique_al((a × d)' + ax0) ∧ (∀ a, d0, d. a × d0 ∈ ax0 ∧ a × d ∈ ax0 ∧ unique_al(ax0) → d = d0) → d1 = d0 ∨ ¬ a0 × d0 ∈ ax0 ∧ a0 × d0 ≠ a × d ∨ ¬ a0 × d1 ∈ ax0 ∧ a0 × d1 ≠ a × d

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;