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Proof step 2 from proof firstn-last-rec (previous step)

n ≤ # x ⊦ firstn(n, x) = firstn(n -1, x) + x[n -1], n = 0

User applied rule structural induction

And obtained the following new goals

Proof step 3:
n0 +1 ≤ # x, ∀ x. n0 ≤ # x → firstn(n0, x) = firstn(n0 -1, x) + x[n0 -1] ∨ n0 = 0 ⊦ n0 +1 = 0, firstn(n0 +1, x) = firstn(n0 +1 -1, x) + x[n0 +1 -1]

Rule argument

indvar: n

Additional information

Used simplifier rules: nat freely generated by 0, +1;;