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Proof step 7 from proof ocs-mklist (previous step)

∀ 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 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
∀ a. x0 = mklist(a, #oc(a, x0)) ↔ x0 -l a = [] ⊦ x0 = mklist(a0, #oc(a0, x0)) ↔ x0 -l a0 = []

Rule argument

Additional information

Used simplifier rules: ⊦ m + 1 ≠ 0; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ x + y = x + z ↔ y = z; (s)% ⊦ a + x = a ' + x; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)