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Proof step 2 from proof lenle (previous step)

# ay < # ax, unique_al(ax.rest), ∀ a. a ∈ ax → a ∈ ay ⊦ ax = [], ax.first.1 ∈ ax.rest

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ ay. # ay < # ax0 ∧ unique_al(ax0.rest) ∧ (∀ a. a ∈ ax0 → a ∈ ay) → ax0 = [] ∨ ax0.first.1 ∈ ax0.rest, # ay < #(p + ax0), unique_al((p + ax0).rest), ∀ a. a ∈ p + ax0 → a ∈ ay ⊦ p + ax0 = [], (p + ax0).first.1 ∈ (p + ax0).rest

Rule argument

indvar: ax

Additional information

Used simplifier rules: assoclist freely generated by [], +;;