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Proof step 11 from proof diffone-nodupsget (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
n = m + 1, a ∈ x0, n < # x0, pos(a, x0) < n, pos(a, x0) + 1 < # x0, ∀ a1, n0. a1 ∈ x0 ∧ n0 + 1 < # x0 → (x0 \ a1 ')[n0] = (n0 < pos(a1, x0) ⊃ x0[n0];x0[n0 + 1]) ⊦ x0 = [], n = 0, (x0 \ a ')[m] = x0[n], a0 ∈ x0, dups(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