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

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2