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Proof step 5 from proof lastn-restn (previous step)

m + n ≤ 1 + # x0, ∀ m, n. m + n ≤ # x0 → lastn(m, restn(n, x0)) = lastn(m, x0) ⊦ lastn(m, restn(n, a ' + x0)) = lastn(m, a ' + x0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 < n → restn(n, x) = restn(n -1, x.tail)
Proof step 7:
0 < n, m + n ≤ 1 + # x0, ∀ m, n. m + n ≤ # x0 → lastn(m, restn(n, x0)) = lastn(m, x0) ⊦ lastn(m, restn(n -1, (a ' + x0).tail)) = lastn(m, a ' + x0)

Rule argument

spec: <toplevel> name: rest-rec seq: ⊦ 0 < n → restn(n, x) = restn(n -1, x.tail) subst: [x, n] → [a ' + x0, n] flags: <all paths>

Additional information

Used simplifier rules: restN-zero: ⊦ restn(0, x) = x;% ⊦ 0 < n ↔ n ≠ 0; (s) Used terms: a ' + x0, n