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Proof step 4 from proof lastn-restn (previous step)

m + n ≤ # x0 + 1, ∀ 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 5:
⊦ 0 < n → restn(n, x) = restn(n -1, x.rest)
Proof step 6:
0 < n, m + n ≤ # x0 + 1, ∀ m, n. m + n ≤ # x0 → lastn(m, restn(n, x0)) = lastn(m, x0) ⊦ lastn(m, restn(n -1, (a ' + x0).rest)) = lastn(m, a ' + x0)

Rule argument

spec: list-del inst: name: rest-rec seq: ⊦ 0 < n → restn(n, x) = restn(n -1, x.rest) subst: [x, n] → [a ' + x0, n] flags: rewrite, current

Additional information

Used simplifier rules: restN-zero: ⊦ restn(0, x) = x;%zero: ⊦ 0 < m ↔ m ≠ 0; from specification nat-basic1 Used terms: a ' + x0, n