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Proof step 1 from proof append-prefix-left (conclusion)

⊦ ar0 + ar1 = ar0 ↔ # ar1 = 0

User applied rule case distinction

And obtained the following new goals

Proof step 2:
ar0 + ar1 = ar0 ⊦ # ar1 = 0
Proof step 6:
# ar1 = 0 ⊦ ar0 + ar1 = ar0

Rule argument

pos: right 1

Additional information