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Proof step 5 from proof nuni-01 (previous step)

p = a1 × d1, a ∈ az, unique_al((p ' + ay0) + (a × d)' + az), ∀ a0, az0, d0. ¬ a0 ∈ az0 ∨ ¬ unique_al(ay0 + (a0 × d0)' + az0) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
a ∈ az, unique_al(ay0 + (a × d)' + az), ∀ a0, az0, d0. ¬ a0 ∈ az0 ∨ ¬ unique_al(ay0 + (a0 × d0)' + az0) ⊦ a1 ∈ az, a1 ∈ ay0

Rule argument

Additional information

Used simplifier rules: cons: ⊦ unique_al((a × d)' + ax) ↔ ¬ a ∈ ax ∧ unique_al(ax);%inapp: ⊦ a ∈ ax + ay ↔ ¬ ¬(a ∈ ax ∨ a ∈ ay);%inone: ⊦ a ∈ (b × d0)' ↔ a = b;%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[assoclista]