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

Rule argument

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