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Proof step 4 from proof mk-inj-01 (previous step)

mklist(a, m0 + 1) = mklist(a, n), ∀ a, n. mklist(a, m0) = mklist(a, n) → m0 = n ⊦ m0 + 1 = n

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:
a + mklist(a, m0 + 1 - 1) = mklist(a, n), ∀ a, n. mklist(a, m0) = mklist(a, n) → m0 = n ⊦ m0 + 1 = n, m0 + 1 = 0

Rule argument

spec: <toplevel> name: mk-rec seq: ⊦ m ≠ 0 → mklist(a, m) = a + mklist(a, m - 1) subst: [m, a] → [m0 + 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: m0 + 1, a