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Proof step 2 from proof k-unique-r (previous step)

ay = p + ax0 ⊦ unique_al(ay) ↔ ay = [] ∨ ¬ p.1 ∈ ax0 ∧ unique_al(ax0), ay = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ unique_al(p ' + ax0) ↔ ¬ p.1 ∈ ax0 ∧ unique_al(ax0)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[assoclist]% ⊦ p ' + ax ≠ []; (s)% ⊦ p + ax = p ' + ax; (s)