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Proof step 3 from proof perm-mklist (previous step)

perm(x, mklist(a, n0 + 1)), perm(mklist(a, n0 + 1), x), ∀ x0, a0. perm(x0, mklist(a0, n0)) → x0 = mklist(a0, n0) ⊦ x = mklist(a, n0 + 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ m ≠ 0 → mklist(a, m) = a + mklist(a, m - 1)
Proof step 5:
n0 + 1 ≠ 0, perm(x, a + mklist(a, n0 + 1 - 1)), perm(a + mklist(a, n0 + 1 - 1), x), ∀ x0, a0. perm(x0, mklist(a0, n0)) → x0 = mklist(a0, n0) ⊦ x = a + mklist(a, n0 + 1 - 1)

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