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Proof step 13 from proof diffone-nodupsget (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
pos(a, x0) + 1 < # x0, m + 1 < # x0, a ∈ x0, pos(a, x0) ≤ m, ∀ n0, a1. n0 + 1 < # x0 ∧ a1 ∈ x0 → (x0 \ a1 ')[n0] = (n0 < pos(a1, x0) ⊃ x0[n0];x0[n0 + 1]) ⊦ (x0 \ a ')[m] = x0[m + 1], x0 = [], dups(x0), a0 ∈ x0

Rule argument

Additional information

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