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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:
perm(a + mklist(a, n0 + 1 - 1), x), perm(x, a + mklist(a, n0 + 1 - 1)), ∀ x0, a0. perm(x0, mklist(a0, n0)) → x0 = mklist(a0, n0) ⊦ n0 + 1 = 0, x = a + mklist(a, n0 + 1 - 1)

Rule argument

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

Additional information

Used simplifier rules: ⊦ m + 1 ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: n0 + 1, a