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Proof step 2 from proof firstrestex (previous step)

n < # x ⊦ x = firstn(n, x) + restn(n, x), x = []

User applied rule structural induction

And obtained the following new goals

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

Rule argument

indvar: n

Additional information

Used simplifier rules: firstN-zero: ⊦ firstn(0, x) = [];%restN-zero: ⊦ restn(0, x) = x;%nat freely generated by 0, +1;;%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list