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Proof step 3 from proof lastN-blastN (previous step)

n ≤ # x, ∀ x0, n. # x0 < # x → n ≤ # x0 → butlastn(n, x0) + lastn(n, x0) = x0 ⊦ butlastn(n, x) + lastn(n, x) = x

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 4:
⊦ x ≠ [] → (∃ y, a. x = y + a ')
Proof step 5:
x ≠ [] → (∃ y, a. x = y + a '), n ≤ # x, ∀ x0, n. # x0 < # x → n ≤ # x0 → butlastn(n, x0) + lastn(n, x0) = x0 ⊦ butlastn(n, x) + lastn(n, x) = x

Rule argument

spec: list inst: name: lastdiv seq: ⊦ x ≠ [] → (∃ y, a. x = y + a ') subst: [x] → [x] flags: []

Additional information

Used terms: x