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Proof step 4 from proof lenle (previous step)

# ay ≤ # ax0, unique_al(p ' + ax0), unique_al(ax0) ∧ (∃ ay0. (∀ a. a ∈ ax0 → a ∈ ay0) ∧ ¬ # ax0 ≤ # ay0) → ax0 = [], ∀ a. a ∈ p ' ∨ a ∈ ax0 → a ∈ ay ⊦

User applied rule structural induction

And obtained the following new goals

Proof step 5:
⊦ ¬ ( # ay ≤ # ax0 ∧ unique_al((a × d)' + ax0) ∧ (unique_al(ax0) ∧ (∃ ay0. (∀ a. a ∈ ax0 → a ∈ ay0) ∧ ¬ # ax0 ≤ # ay0) → ax0 = []) ∧ (∀ a0. a0 ∈ (a × d)' ∨ a0 ∈ ax0 → a0 ∈ ay))

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;