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Proof step 7 from proof uniquelen (previous step)

ay = p + ax0, unique_al(ax0), ∀ a. ¬ a ∈ ay ⊦ ay = [], p.1 ∈ ax0, p.1 ∈ ay

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
unique_al(ax0), ∀ a. ¬ a ∈ p ' ∧ ¬ a ∈ ax0 ⊦ p.1 ∈ ax0, p.1 ∈ p '

Rule argument

Additional information

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