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Proof step 1 from proof fill-append-shift (conclusion)

⊦ # ar0 ≤ n → fill(ar0 + ar1, a, n, m) = ar0 + fill(ar1, a, n - # ar0, m)

System applied rule normalize

And obtained the following new goals

Proof step 2:
# ar0 ≤ n ⊦ fill(ar0 + ar1, a, n, m) = ar0 + fill(ar1, a, n - # ar0, m)

Rule argument

Additional information