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Proof step 20 from proof rmpos-in (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
n = m + 1, n ≤ # x0, x0[m] ∈ (a0 ' + x0) -1l n, x0[m] ∈ x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -1l n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0) ⊦ x0 = [], n = 0, dups(x0), a0 ∈ x0

Rule argument

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

Additional information

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