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Proof step 5 from proof ocs-mklist (previous step)

∀ a. x0 = mklist(a, #oc(a, x0)) ↔ x0 -l a = [] ⊦ a0 ' + x0 = mklist(a0, 1 + #oc(a0, x0)) ↔ x0 -l a0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ m ≠ 0 → mklist(a, m) = a + mklist(a, m - 1)
Proof step 7:
∀ a. x0 = mklist(a, #oc(a, x0)) ↔ x0 -l a = [] ⊦ 1 + #oc(a0, x0) = 0, a0 ' + x0 = a0 + mklist(a0, 1 + #oc(a0, x0) - 1) ↔ x0 -l a0 = []

Rule argument

spec: list-last name: mk-rec seq: ⊦ m ≠ 0 → mklist(a, m) = a + mklist(a, m - 1) subst: [m, a] → [1 + #oc(a0, x0), a0] 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: 1 + #oc(a0, x0), a0