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Proof step 2 from proof app (previous step)

unique_al(ax + p ' + ay) ⊦ ax + ay = [], ¬ (ax + ay).first.1 ∈ (ax + ay).rest ∧ unique_al((ax + ay).rest)

User applied rule structural induction

And obtained the following new goals

Proof step 3:
unique_al([] + p ' + ay) ⊦ [] + ay = [], ¬ ([] + ay).first.1 ∈ ([] + ay).rest ∧ unique_al(([] + ay).rest)
Proof step 6:
∀ p, ay. unique_al(ax0 + p ' + ay) → ax0 + ay = [] ∨ ¬ (ax0 + ay).first.1 ∈ (ax0 + ay).rest ∧ unique_al((ax0 + ay).rest), unique_al((p0 + ax0) + p ' + ay) ⊦ (p0 + ax0) + ay = [], ¬ ((p0 + ax0) + ay).first.1 ∈ ((p0 + ax0) + ay).rest ∧ unique_al(((p0 + ax0) + ay).rest)

Rule argument

indvar: ax

Additional information

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