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Proof step 3 from proof nuni (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

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;