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Proof step 19 from proof uniquelen (previous step)

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 ⊦ # ax0 = # ay0 + # az, a0 ∈ ax0 ↔ a0 ∈ ay0 ∨ a0 ∈ az, a ∈ ax0, a ∈ az

User applied rule case distinction

And obtained the following new goals

Proof step 20:
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

Rule argument

pos: right 2

Proof step 19 from proof uniquelen (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information