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Proof step 6 from proof uniquelen (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
unique_al(p ' + ax), ∀ a. ¬ a ∈ p ' ∧ ¬ a ∈ ax ⊦ p.1 ∈ ax, p.1 ∈ p '

Rule argument

Additional information

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