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Proof step 1 from proof diffone-nodupsget (conclusion)

⊦ n + 1 < # x ∧ ¬ dups(x) ∧ a ∈ x → (x \ a ')[n] = (n < pos(a, x) ⊃ x[n];x[n + 1])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
a ∈ x, n + 1 < # x ⊦ (x \ a ')[n] = (n < pos(a, x) ⊃ x[n];x[n + 1]), x = [], dups(x)

Rule argument

Additional information

Used simplifier rules: l: ⊦ # x = 0 ↔ x = []; from specification list-data%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1