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Proof step 3 from proof app (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
unique_al(p ' + ay) ⊦ ay = [], ¬ ay.first.1 ∈ ay.rest ∧ unique_al(ay.rest)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[assoclista]%Nil: ⊦ [] + ax = ax; from specification list[assoclista]