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

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)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 5 terms: a, m

Additional information

Used simplifier rules: le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat Used terms: a, m