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Proof step 2 from proof firstN-num-rec (previous step)

n ≠ 0 ⊦ firstn(n, a ' + x) = a ' + firstn(n -1, x)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ n = 0, firstn(n, a ' + x) = a ' + firstn(n - 1, x)

Rule argument

Additional information

Used simplifier rules: pred-03: ⊦ n -1 = n - 1; from specification nat