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Proof step 34 from proof rmpos-in (previous step)

a ∈ x0, n ≤ # x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -p n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0) ⊦ a = x0[n - 1], n = 0, x0 = [], dups(x0), a ∈ (a0 ' + x0) -p n, a0 ∈ x0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 35:
n = m + 1, a ∈ x0, n ≤ # x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -p n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0) ⊦ a = x0[m], n = 0, x0 = [], dups(x0), a0 ∈ x0, a ∈ (a0 ' + x0) -p n

Rule argument

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

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m