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Proof step 12 from proof perm-put-del1 (previous step)

n < # y, y[n] ∈ y, y[n] ∈ y[n, a] -1l a ∨ y[n] ∈ y -1l y[n] ⊦ #oc(y[n], y[n, a] -1l a) = #oc(y[n], y) - 1, y = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
#oc(y[n], y) = m + 1, n < # y, y[n] ∈ y, y[n] ∈ y[n, a] -1l a ∨ y[n] ∈ y -1l y[n] ⊦ #oc(y[n], y[n, a] -1l a) = m, #oc(y[n], y) = 0, y = []

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [#oc(y[n], y), m]

Additional information

Used simplifier rules: in-05: ⊦ a ∈ x → #oc(a, x) ≠ 0;%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: #oc(y[n], y), m