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Proof step 9 from proof uniquelen (previous step)

unique_al(ay), unique_al(p ' + ax0), ∀ ay. (∀ a. a ∈ ax0 ↔ a ∈ ay) ∧ unique_al(ax0) ∧ unique_al(ay) → # ax0 = # ay, ∀ a. a ∈ p ' ∨ a ∈ ax0 ↔ a ∈ ay ⊦ 1 + # ax0 = # ay

User applied rule structural induction

And obtained the following new goals

Proof step 10:
⊦ unique_al(ay) ∧ unique_al((a × d)' + ax0) ∧ (∀ ay. (∀ a. a ∈ ax0 ↔ a ∈ ay) ∧ unique_al(ax0) ∧ unique_al(ay) → # ax0 = # ay) ∧ (∀ a0. a0 ∈ (a × d)' ∨ a0 ∈ ax0 ↔ a0 ∈ ay) → 1 + # ax0 = # ay

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;