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Proof step 3 from proof firstN-lastN-in (previous step)

a ∈ x, n ≤ # x ⊦ a ∈ lastn(n, x), a ∈ firstn(# x - n, x)

User applied rule apply lemma

And obtained the following new goals

Proof step 4:
⊦ n ≤ # x → firstn(# x - n, x) + lastn(n, x) = x
Proof step 5:
a ∈ x, n ≤ # x, n ≤ # x → firstn(# x - n, x) + lastn(n, x) = x ⊦ a ∈ firstn(# x - n, x), a ∈ lastn(n, x)

Rule argument

spec: <toplevel> name: firstN-lastN seq: ⊦ n ≤ # x → firstn(# x - n, x) + lastn(n, x) = x subst: [n, x] → [n, x]

Additional information

Used terms: n, x