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Proof step 3 from proof nuni-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
a ∈ az, unique_al((p ' + ax) + (a × d)' + az), ∀ a0, d0, az0. ¬ unique_al(ax + (a0 × d0)' + az0) ∨ ¬ a0 ∈ az0 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ p + ax = p ' + ax;