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Proof step 10 from proof app (previous step)

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

User applied rule all left

And closed the goal!

Rule argument

pos: left 2 terms: p, ay abort: F discard: F computed: T

Additional information

Used simplifier rules: a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[assoclista] Used terms: p, ay