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Proof step 8 from proof in-prefixn-in-shorter-prefix (previous step)

a ∈ y, n1 ≤ # y + # z, # y ≤ n1 ⊦ a ∈ firstn(n1, y + z)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ # x ≤ n → firstn(n, x + y) = x + firstn(n - # x, y)

Rule argument

spec: list-del name: firstn-app-01 seq: ⊦ # x ≤ n → firstn(n, x + y) = x + firstn(n - # x, y) subst: [y, x, n] → [z, y, n1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ a ∈ x → a ∈ x + y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: z, y, n1