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Proof step 2 from proof diffone-nodupsget (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n + 1 < # x, a ∈ x ⊦ (x \ a ')[n] = (n < pos(a, x) ⊃ x[n];x[n + 1]), x = [], dups(x)

Rule argument

Additional information

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