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Proof step 12 from proof diffone-nodupsget (previous step)

n < # x0, pos(a, x0) < n, pos(a, x0) + 1 < # x0, a ∈ x0, ∀ n0, a1. n0 + 1 < # x0 ∧ a1 ∈ x0 → (x0 \ a1 ')[n0] = (n0 < pos(a1, x0) ⊃ x0[n0];x0[n0 + 1]) ⊦ (x0 \ a ')[n - 1] = x0[n], x0 = [], dups(x0), a0 ∈ x0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
n = m + 1, pos(a, x0) + 1 < # x0, pos(a, x0) < n, n < # x0, a ∈ x0, ∀ n0, a1. n0 + 1 < # x0 ∧ a1 ∈ x0 → (x0 \ a1 ')[n0] = (n0 < pos(a1, x0) ⊃ x0[n0];x0[n0 + 1]) ⊦ (x0 \ a ')[m] = x0[n], n = 0, x0 = [], dups(x0), a0 ∈ x0

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: ⊦ x ≠ [] → x[0] = x.head; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ # x = 0 ↔ x = []; (s)% ⊦ ¬ m < 0; (s)%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m