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Proof step 4 from proof first-mklist (previous step)

m ≤ n0 + 1, ∀ m, a. m ≤ n0 → firstn(m, mklist(a, n0)) = mklist(a, m) ⊦ firstn(m, mklist(a, n0 + 1)) = mklist(a, m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ m ≠ 0 → mklist(a, m) = a + mklist(a, m - 1)
Proof step 6:
n0 + 1 ≠ 0, m ≤ n0 + 1, ∀ m, a. m ≤ n0 → firstn(m, mklist(a, n0)) = mklist(a, m) ⊦ firstn(m, a + mklist(a, n0 + 1 - 1)) = mklist(a, m)

Rule argument

spec: list-last inst: name: mk-rec seq: ⊦ m ≠ 0 → mklist(a, m) = a + mklist(a, m - 1) subst: [m, a] → [n0 + 1, a] flags: rewrite

Additional information

Used simplifier rules: z-01: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: n0 + 1, a