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Proof step 20 from proof uniquelen (previous step)

a0 ∈ ay0 ∨ a0 ∈ az, unique_al(ax0), unique_al(ay0 + (a × d)' + az), a0 ∈ ax0 ∨ a0 = a ↔ a0 ∈ az ∨ a0 = a ∨ a0 ∈ ay0, ∀ a0. a0 ∈ ax0 ∨ a0 = a ↔ a0 ∈ az ∨ a0 = a ∨ a0 ∈ ay0 ⊦ a0 ∈ ax0, # ax0 = # ay0 + # az, a ∈ ax0, a ∈ az

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: nuni: ⊦ unique_al(ay + (a × d)' + az) → ¬ a ∈ ay;% ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1;