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Proof step 3 from proof nuni (previous step)

∀ a, d, az. a ∈ ay0 ∧ unique_al(ay0 + (a × d)' + az) → a ∈ az, a ∈ p + ay0, unique_al((p + ay0) + (a × d)' + az) ⊦ a ∈ az

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
unique_al((p ' + ay0) + (a × d)' + az), ∀ a, d, az. a ∈ ay0 ∧ unique_al(ay0 + (a × d)' + az) → a ∈ az, a ∈ p ' ∨ a ∈ ay0 ⊦ a ∈ az

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[assoclista]%c: ⊦ p + ax = p ' + ax; from specification list[assoclista]